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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "0",
+   "metadata": {},
+   "source": [
+    "# Palace 2D Mode Analysis: Travelling-Wave Mach-Zehnder Modulator\n",
+    "\n",
+    "This notebook builds a simplified cross-section of a Travelling-Wave Mach-Zehnder Modulator (TW-MZM) with a PN-junction embedded in a rib waveguide, using CPW electrodes for RF modulation.\n",
+    "\n",
+    "**Cross-section geometry (from literature):**\n",
+    "- **SOI substrate**: 220 nm Si on 2 um buried oxide (BOX)\n",
+    "- **Rib waveguide**: 400 nm width, 90 nm slab height\n",
+    "- **CPW electrodes**: Aluminium, 1 um thick, signal width $w=20$ um, gap $g=20$ um\n",
+    "- **PN junction**: Centred in the rib with P+/N+ contact regions in the slab\n",
+    "\n",
+    "We use `BoundaryModeSim` (Palace 2D eigenmode solver) to compute both RF and optical modes.\n",
+    "\n",
+    "**Requirements:**\n",
+    "- gdsfactory + generic PDK (`gf.gpdk`)\n",
+    "- A Palace binary resolved internally by `run_local()` (e.g. `palace-toolkit-cpu`, `PALACE_BIN`, or `palace` on PATH)\n",
+    "- [GDSFactory+](https://gdsfactory.com) account only for cloud runs\n",
+    "\n",
+    "**Workflow:** parameters are grouped next to the stage they configure — geometry & materials, then RF, then optical.\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1",
+   "metadata": {},
+   "source": [
+    "## Geometry & materials parameters\n",
+    "\n",
+    "Define the layout dimensions, the substrate/metal stack, and the doping\n",
+    "(geometry + material) for the rib and graded slab regions. These are consumed\n",
+    "by the geometry build and by\n",
+    "`gsim.common.cross_section.build_doped_cross_section()`.\n",
+    "\n",
+    "The generic helpers used here are PDK-agnostic — no hardcoded values live in\n",
+    "the notebook.\n",
+    "\n",
+    "**Layer assignments (gpdk):**\n",
+    "- `WG` (1,0): Waveguide core (220 nm Si, 400 nm wide)\n",
+    "- `SLAB90` (3,0): 90 nm slab regions\n",
+    "- `N` (20,0) / `P` (21,0): PN junction doping\n",
+    "- `NPP` (24,0) / `PP` (23,0): N+/P+ graded contact doping (via `make_doping_profile`)\n",
+    "- `M1` (41,0): CPW electrodes (Al, 1 um thick)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# =============================================================================\n",
+    "#  Geometry & materials parameters\n",
+    "# =============================================================================\n",
+    "\n",
+    "# --- Device / rib geometry (um) ---------------------------------------------\n",
+    "RIB_WIDTH = 0.4  # rib waveguide width\n",
+    "RIB_HEIGHT = 0.22  # rib waveguide height (z)\n",
+    "SLAB_THICKNESS = 0.09  # slab height (z) on each side of the rib\n",
+    "SLAB_HALF = 50.0  # slab half-width (y, on each side of the rib)\n",
+    "SIG_WIDTH = 20.0  # CPW signal electrode width\n",
+    "GAP_WIDTH = 20.0  # CPW signal-to-ground gap\n",
+    "GND_WIDTH = 40.0  # CPW ground electrode width\n",
+    "LENGTH = 10.0  # layout length along the propagation axis (x)\n",
+    "TOTAL_HALF = SIG_WIDTH / 2 + GAP_WIDTH + GND_WIDTH  # lateral half-extent\n",
+    "RIB_CENTER_Y = -(SIG_WIDTH / 2 + GAP_WIDTH / 2)  # rib centre y (=-20)\n",
+    "\n",
+    "VIA_SIZE = 2.7  # via_stack footprint (square)\n",
+    "VIA_S_TO_P_Y = -9.0  # via from signal to P+ contact (y)\n",
+    "VIA_G_TO_N_Y = -29.0  # via from ground to N+ contact (y)\n",
+    "\n",
+    "# --- Substrate stack (um) -----------------------------------------------------\n",
+    "BOX_THICKNESS = 2.0  # buried-oxide thickness (below z=0)\n",
+    "METAL1_ZMIN = 1.1  # metal1 bottom (top of the oxide stack)\n",
+    "METAL1_THICKNESS = 1.0  # CPW electrode thickness on metal1\n",
+    "\n",
+    "# --- PN junction / doping material model -------------------------------------\n",
+    "SI_PERMITTIVITY = 11.9\n",
+    "FMAX_RF_MATERIAL = 200e9  # validity range of the constant-eps doping models (Hz)\n",
+    "RIB_DOPING_SIGMA = 1.6e3  # p_rib / n_rib junction conductivity (S/m)\n",
+    "\n",
+    "# Graded slab doping {side: [(width_um, sigma_S_per_m), ...]}, from the rib edge.\n",
+    "DOPING_PROFILE = {\n",
+    "    \"upper\": [(2.0, 2.0e4), (2.0, 8.0e4)],  # P+ graded (toward signal)\n",
+    "    \"lower\": [(2.0, 2.0e4), (2.0, 8.0e4)],  # N+ graded (toward ground)\n",
+    "}\n",
+    "DOPING_SIDES = {  # config passed to make_doping_profile()\n",
+    "    \"upper\": {\"base_layer\": (23, 0), \"name_prefix\": \"pp_slab_\", \"sign\": 1},\n",
+    "    \"lower\": {\"base_layer\": (24, 0), \"name_prefix\": \"npp_slab_\", \"sign\": -1},\n",
+    "}\n",
+    "\n",
+    "# --- Cross-section plane ------------------------------------------------------\n",
+    "CROSS_SECTION_AXIS = \"x\"\n",
+    "CROSS_SECTION_VALUE = 0.0"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3",
+   "metadata": {},
+   "source": [
+    "## Build TW-MZM cross-section geometry\n",
+    "\n",
+    "The 3D layout component is sliced at $x=0$ for 2D mode analysis. The graded\n",
+    "doping regions are created with `make_doping_profile()` (no hardcoded geometry).\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "4",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 800x600 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import gdsfactory as gf\n",
+    "\n",
+    "from gsim.common.cross_section import build_optical_cross_section\n",
+    "from gsim.common.stack.doping import make_doping_profile\n",
+    "\n",
+    "gf.gpdk.PDK.activate()\n",
+    "\n",
+    "LAYER = gf.gpdk.LAYER\n",
+    "\n",
+    "\n",
+    "def centered_rect(wx: float, wy: float, layer) -> gf.Component:\n",
+    "    r = gf.Component()\n",
+    "    r << gf.c.rectangle((wx, wy), centered=True, layer=layer)\n",
+    "    return r\n",
+    "\n",
+    "\n",
+    "def _add_device_core(comp: gf.Component) -> None:\n",
+    "    \"\"\"Rib + slab + PN junction — shared by the RF and optical components.\n",
+    "\n",
+    "    The P/N rectangles are the same \"doping profile\" polygons in both, so the\n",
+    "    optical cross-section still shows the junction shape. The optical stack\n",
+    "    maps all four regions to plain silicon.\n",
+    "    \"\"\"\n",
+    "    # 1. Rib waveguide core (PN junction sits inside it)\n",
+    "    wg = comp << centered_rect(LENGTH, RIB_WIDTH, LAYER.WG)\n",
+    "    wg.y = RIB_CENTER_Y\n",
+    "\n",
+    "    # 2. Slab (90 nm)\n",
+    "    slab = comp << centered_rect(LENGTH, 2 * SLAB_HALF + RIB_WIDTH, LAYER.SLAB90)\n",
+    "    slab.y = 0.0\n",
+    "\n",
+    "    # 3. PN junction (P above / N below the rib centre)\n",
+    "    p_half = comp << gf.c.rectangle((LENGTH, RIB_WIDTH / 2), layer=LAYER.P)\n",
+    "    p_half.y = RIB_CENTER_Y + RIB_WIDTH / 4\n",
+    "    n_half = comp << gf.c.rectangle((LENGTH, RIB_WIDTH / 2), layer=LAYER.N)\n",
+    "    n_half.y = RIB_CENTER_Y - RIB_WIDTH / 4\n",
+    "\n",
+    "\n",
+    "def _build_rf_component() -> tuple[gf.Component, dict]:\n",
+    "    \"\"\"Full TW-MZM cross-section: device core + graded doping + CPW + vias.\"\"\"\n",
+    "    comp = gf.Component()\n",
+    "    _add_device_core(comp)\n",
+    "\n",
+    "    # 4. Graded N+/P+ slab doping (contiguous, no gaps)\n",
+    "    doping_result = make_doping_profile(\n",
+    "        comp,\n",
+    "        length=LENGTH,\n",
+    "        rib_center_y=RIB_CENTER_Y,\n",
+    "        rib_width=RIB_WIDTH,\n",
+    "        profile=DOPING_PROFILE,\n",
+    "        sides=DOPING_SIDES,\n",
+    "        zmin=0.0,\n",
+    "        zmax=SLAB_THICKNESS,\n",
+    "        permittivity=SI_PERMITTIVITY,\n",
+    "        fmax=FMAX_RF_MATERIAL,\n",
+    "    )\n",
+    "\n",
+    "    # 5. CPW electrodes (M1)\n",
+    "    comp << centered_rect(LENGTH, SIG_WIDTH, LAYER.M1)\n",
+    "    gnd_top = comp << centered_rect(LENGTH, GND_WIDTH, LAYER.M1)\n",
+    "    gnd_top.y = SIG_WIDTH / 2 + GAP_WIDTH + GND_WIDTH / 2\n",
+    "    gnd_bot = comp << centered_rect(LENGTH, GND_WIDTH, LAYER.M1)\n",
+    "    gnd_bot.y = -(SIG_WIDTH / 2 + GAP_WIDTH + GND_WIDTH / 2)\n",
+    "\n",
+    "    # 6. Vias at x=0 (signal-to-P+, ground-to-N+)\n",
+    "    via_s_to_p = comp << gf.c.via_stack(\n",
+    "        layers=(\"SLAB90\", \"M1\"), vias=(\"viac\", None), size=(VIA_SIZE, VIA_SIZE)\n",
+    "    )\n",
+    "    via_s_to_p.x = 0.0\n",
+    "    via_s_to_p.y = VIA_S_TO_P_Y\n",
+    "\n",
+    "    via_g_to_n = comp << gf.c.via_stack(\n",
+    "        layers=(\"SLAB90\", \"M1\"), vias=(\"viac\", None), size=(VIA_SIZE, VIA_SIZE)\n",
+    "    )\n",
+    "    via_g_to_n.x = 0.0\n",
+    "    via_g_to_n.y = VIA_G_TO_N_Y\n",
+    "\n",
+    "    return comp, doping_result\n",
+    "\n",
+    "\n",
+    "def _build_optical_component() -> gf.Component:\n",
+    "    \"\"\"Optical-only cross-section: rib + slab + PN junction (all silicon).\n",
+    "\n",
+    "    No electrodes, vias, or graded doping — the optical mode sees a single\n",
+    "    homogeneous Si body embedded in the uniform SiO2 cladding stack.\n",
+    "    \"\"\"\n",
+    "    comp = gf.Component()\n",
+    "    _add_device_core(comp)\n",
+    "    return comp\n",
+    "\n",
+    "\n",
+    "# --- RF component (electrodes, vias, graded doping) ------------------------\n",
+    "comp, doping_result = _build_rf_component()\n",
+    "\n",
+    "# --- Optical component (rib + slab + PN junction only) ---------------------\n",
+    "comp_optical = _build_optical_component()\n",
+    "\n",
+    "# -- Plot ----------------------------------------------------------------------\n",
+    "_cc = comp.copy()\n",
+    "_cc.draw_ports()\n",
+    "_cc.plot()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5",
+   "metadata": {},
+   "source": [
+    "## Inspect 2D cross-section\n",
+    "\n",
+    "The reusable `gsim.common.cross_section.build_doped_cross_section()` helper\n",
+    "assembles the base PDK stack, overrides `metal1`, registers the gradient doping\n",
+    "and PN-junction rib layers, and extracts the 2D cross-section at $x=0$.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "6",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "INFO M1 updated: zmin=1.1, zmax=2.1, thickness=1.0\n",
+      "INFO Stack: generic\n",
+      "INFO Layers: ['box', 'clad', 'core', 'deep_etch', 'ge', 'heater', 'metal1', 'metal2', 'metal3', 'n_rib', 'nitride', 'npp_slab_0', 'npp_slab_1', 'p_rib', 'pp_slab_0', 'pp_slab_1', 'shallow_etch', 'slab150', 'slab90', 'undercut', 'via1', 'via2', 'via_contact']\n",
+      "INFO Cross materials: ['n_rib', 'npp_slab_0', 'npp_slab_1', 'p_rib', 'pp_slab_0', 'pp_slab_1']\n",
+      "INFO Dielectrics: [{'name': 'oxide', 'zmin': -2.0, 'zmax': 5.2, 'material': 'sio2'}, {'name': 'passive', 'zmin': 5.2, 'zmax': 5.6000000000000005, 'material': 'passive'}]\n",
+      "INFO \n",
+      "INFO Cross-section x=0.0 intersects 13 layer regions:\n",
+      "INFO   core         material=si         y=[ -20.200,  -19.800]  z=[ 0.000,  0.220]\n",
+      "INFO   slab90       material=si         y=[ -50.200,   50.200]  z=[ 0.000,  0.090]\n",
+      "INFO   via_contact  material=Aluminum   y=[ -29.350,  -28.650]  z=[ 0.090,  1.100]\n",
+      "INFO   via_contact  material=Aluminum   y=[  -9.350,   -8.650]  z=[ 0.090,  1.100]\n",
+      "INFO   metal1       material=Aluminum   y=[ -70.000,  -27.650]  z=[ 1.100,  2.100]\n",
+      "INFO   metal1       material=Aluminum   y=[ -10.350,   10.000]  z=[ 1.100,  2.100]\n",
+      "INFO   metal1       material=Aluminum   y=[  30.000,   70.000]  z=[ 1.100,  2.100]\n",
+      "INFO   pp_slab_0    material=pp_slab_0  y=[ -19.800,  -17.800]  z=[ 0.000,  0.090]\n",
+      "INFO   pp_slab_1    material=pp_slab_1  y=[ -17.800,  -15.800]  z=[ 0.000,  0.090]\n",
+      "INFO   npp_slab_0   material=npp_slab_0 y=[ -22.200,  -20.200]  z=[ 0.000,  0.090]\n",
+      "INFO   npp_slab_1   material=npp_slab_1 y=[ -24.200,  -22.200]  z=[ 0.000,  0.090]\n",
+      "INFO   p_rib        material=p_rib      y=[ -20.000,  -19.800]  z=[ 0.000,  0.220]\n",
+      "INFO   n_rib        material=n_rib      y=[ -20.200,  -20.000]  z=[ 0.000,  0.220]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Make the helper's diagnostics visible\n",
+    "import logging\n",
+    "\n",
+    "logging.basicConfig(level=logging.INFO, format=\"%(levelname)s %(message)s\")\n",
+    "\n",
+    "from gsim.common.cross_section import build_doped_cross_section\n",
+    "\n",
+    "stack, section = build_doped_cross_section(\n",
+    "    comp,\n",
+    "    axis=CROSS_SECTION_AXIS,\n",
+    "    value=CROSS_SECTION_VALUE,\n",
+    "    substrate_thickness=BOX_THICKNESS,\n",
+    "    metal1=(METAL1_ZMIN, METAL1_THICKNESS),\n",
+    "    doping=doping_result,\n",
+    "    rib_layers=[\n",
+    "        (\"p_rib\", LAYER.P, RIB_DOPING_SIGMA),\n",
+    "        (\"n_rib\", LAYER.N, RIB_DOPING_SIGMA),\n",
+    "    ],\n",
+    "    rib_height=RIB_HEIGHT,\n",
+    "    permittivity=SI_PERMITTIVITY,\n",
+    "    fmax=FMAX_RF_MATERIAL,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3a9abd45",
+   "metadata": {},
+   "source": [
+    "## Optical-only cross-section\n",
+    "\n",
+    "The optical analysis uses a simplified component: the same rib + slab + PN\n",
+    "junction (identical \"doping profile\" polygons) but **no** electrodes, vias, or\n",
+    "graded doping. Every device region maps to plain silicon, so the optical mode\n",
+    "sees one homogeneous Si body embedded in a uniform SiO2 cladding.\n",
+    "\n",
+    "`gsim.common.cross_section.build_optical_cross_section()` assembles the\n",
+    "minimal all-dielectric `LayerStack` and extracts the 2D cross-section at $x=0$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "7474139a",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "INFO Stack: optical\n",
+      "INFO Layers: ['core', 'n_rib', 'p_rib', 'slab']\n",
+      "INFO Device material: si\n",
+      "INFO Cladding material: sio2\n",
+      "INFO Dielectrics: [{'name': 'oxide', 'zmin': -2.0, 'zmax': 3.0, 'material': 'sio2'}]\n",
+      "INFO \n",
+      "INFO Cross-section x=0.0 intersects 4 layer regions:\n",
+      "INFO   core         material=si         y=[ -20.200,  -19.800]  z=[ 0.000,  0.220]\n",
+      "INFO   slab         material=si         y=[ -50.200,   50.200]  z=[ 0.000,  0.090]\n",
+      "INFO   p_rib        material=si         y=[ -20.000,  -19.800]  z=[ 0.000,  0.220]\n",
+      "INFO   n_rib        material=si         y=[ -20.200,  -20.000]  z=[ 0.000,  0.220]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Optical stack layers: ['core', 'n_rib', 'p_rib', 'slab']\n",
+      "Optical cladding: [{'name': 'oxide', 'zmin': -2.0, 'zmax': 3.0, 'material': 'sio2'}]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Uniform SiO2 cladding height above z=0 (um)\n",
+    "OPT_CLAD_TOP = 3.0\n",
+    "\n",
+    "stack_opt, section_opt = build_optical_cross_section(\n",
+    "    comp_optical,\n",
+    "    axis=CROSS_SECTION_AXIS,\n",
+    "    value=CROSS_SECTION_VALUE,\n",
+    "    device_layers={\n",
+    "        \"core\": (LAYER.WG, 0.0, RIB_HEIGHT),\n",
+    "        \"slab\": (LAYER.SLAB90, 0.0, SLAB_THICKNESS),\n",
+    "        \"p_rib\": (LAYER.P, 0.0, RIB_HEIGHT),\n",
+    "        \"n_rib\": (LAYER.N, 0.0, RIB_HEIGHT),\n",
+    "    },\n",
+    "    substrate_thickness=BOX_THICKNESS,\n",
+    "    cladding_top=OPT_CLAD_TOP,\n",
+    ")\n",
+    "\n",
+    "print(\"Optical stack layers:\", sorted(stack_opt.layers.keys()))\n",
+    "print(\"Optical cladding:\", stack_opt.dielectrics)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "71bcea16",
+   "metadata": {},
+   "source": [
+    "### Optical cross-section plot\n",
+    "\n",
+    "The PN junction still shows its P/N profile, but both regions and the slab are\n",
+    "the same silicon material."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "518d76a7",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 1000x400 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "from gsim.palace import plot_plane_section\n",
+    "\n",
+    "PLOT_ZOOM_OPT = {\"h_range\": (-4.0, 4.0), \"v_range\": (-0.6, 1.5)}\n",
+    "PLOT_COLORS_OPT = {\n",
+    "    \"core\": \"#c0392b\",  # rib Si\n",
+    "    \"slab\": \"#e67e22\",  # slab Si\n",
+    "    \"p_rib\": \"#2980b9\",  # PN junction P region (Si)\n",
+    "    \"n_rib\": \"#27ae60\",  # PN junction N region (Si)\n",
+    "}\n",
+    "PLOT_TITLE_OPT = (\n",
+    "    \"Optical cross-section: rib + slab + PN junction (all Si, SiO2 cladding)\"\n",
+    ")\n",
+    "\n",
+    "plot_plane_section(\n",
+    "    section_opt,\n",
+    "    colors=PLOT_COLORS_OPT,\n",
+    "    h_range=PLOT_ZOOM_OPT[\"h_range\"],\n",
+    "    v_range=PLOT_ZOOM_OPT[\"v_range\"],\n",
+    "    title=PLOT_TITLE_OPT,\n",
+    ")\n",
+    "plt.tight_layout()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9a8a7a82",
+   "metadata": {},
+   "source": [
+    "### Optical material properties (1550 nm)\n",
+    "\n",
+    "The PDK stack materials resolve to their Sellmeier optical constants at the\n",
+    "simulation wavelength. The Palace boundary-mode config generator evaluates\n",
+    "dispersion at `F_OPT` automatically; the values below are for reference."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "22caa2d7",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "si   @ 1.55 um: eps=12.0946  n=3.4777\n",
+      "sio2 @ 1.55 um: eps=2.0852  n=1.4440\n"
+     ]
+    }
+   ],
+   "source": [
+    "import math\n",
+    "\n",
+    "from gsim.common.stack.materials import resolve_material_at_wavelength\n",
+    "\n",
+    "LAMBDA_OPT = 1.55  # reference wavelength (um)\n",
+    "\n",
+    "si_opt = resolve_material_at_wavelength(\"si\", LAMBDA_OPT)\n",
+    "sio2_opt = resolve_material_at_wavelength(\"sio2\", LAMBDA_OPT)\n",
+    "print(\n",
+    "    f\"si   @ {LAMBDA_OPT:.2f} um: eps={si_opt.permittivity_scalar:.4f}  n={math.sqrt(si_opt.permittivity_scalar):.4f}\"\n",
+    ")\n",
+    "print(\n",
+    "    f\"sio2 @ {LAMBDA_OPT:.2f} um: eps={sio2_opt.permittivity_scalar:.4f}  n={math.sqrt(sio2_opt.permittivity_scalar):.4f}\"\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7",
+   "metadata": {},
+   "source": [
+    "## Plot the 2D cross-section\n",
+    "\n",
+    "The physical-group regions are rendered with the reusable\n",
+    "`gsim.palace.plot_plane_section()`. The full layout spans ~140 um, so we zoom\n",
+    "on the central region to show the rib, PN junction, graded doping and vias.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# --- Cross-section plot parameters (physical-group regions) ---------------\n",
+    "PLOT_ZOOM = {\"h_range\": (-15.0, 15.0), \"v_range\": (-0.5, 5.0)}\n",
+    "PLOT_COLORS = {\n",
+    "    \"core\": \"#c0392b\",  # rib Si -- red\n",
+    "    \"slab90\": \"#e67e22\",  # slab Si -- orange\n",
+    "    \"p_rib\": \"#2980b9\",  # P doping -- blue\n",
+    "    \"pp_slab_0\": \"#8e44ad\",  # P+ graded inner -- purple\n",
+    "    \"pp_slab_1\": \"#a569bd\",  # P+ graded outer -- light purple\n",
+    "    \"n_rib\": \"#27ae60\",  # N doping -- green\n",
+    "    \"npp_slab_0\": \"#4460ad\",  # N+ graded inner -- indigo\n",
+    "    \"npp_slab_1\": \"#5b7dcf\",  # N+ graded outer -- light indigo\n",
+    "    \"metal1\": \"#7f8c8d\",  # CPW electrodes (Al) -- grey\n",
+    "    \"metal2\": \"#7f8c8d\",\n",
+    "    \"metal3\": \"#7f8c8d\",\n",
+    "    \"via_contact\": \"#f1c40f\",  # via -- gold\n",
+    "    \"via1\": \"#f1c40f\",\n",
+    "    \"via2\": \"#f1c40f\",\n",
+    "}\n",
+    "PLOT_TITLE = \"TW-MZM cross-section (zoomed on rib + doping + signal electrode)\""
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 1000x400 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "from gsim.palace import plot_plane_section\n",
+    "\n",
+    "plot_plane_section(\n",
+    "    section,\n",
+    "    colors=PLOT_COLORS,\n",
+    "    h_range=PLOT_ZOOM[\"h_range\"],\n",
+    "    v_range=PLOT_ZOOM[\"v_range\"],\n",
+    "    title=PLOT_TITLE,\n",
+    ")\n",
+    "plt.tight_layout()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "10",
+   "metadata": {},
+   "source": [
+    "## RF simulation (50 GHz)\n",
+    "\n",
+    "Configure the 50 GHz BoundaryMode run: simulation airbox, mesh, number of\n",
+    "modes, output directory, and the field quantities to plot.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "11",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# =============================================================================\n",
+    "#  RF parameters (50 GHz BoundaryMode run)\n",
+    "# =============================================================================\n",
+    "\n",
+    "# --- Simulation box (airbox + mesh margins, um) -----------------------------\n",
+    "AIRBOX = {\"margin_x\": 50.0, \"margin_y\": 50.0, \"z_above\": 100.0, \"z_below\": 100.0}\n",
+    "MESH_MARGIN_X = 0.0\n",
+    "MESH_MARGIN_Y = 50.0\n",
+    "\n",
+    "# --- RF solver settings -----------------------------------------------------\n",
+    "F_RF = 50e9\n",
+    "NUM_RF_MODES = 2\n",
+    "RF_OUTPUT_DIR = \"./palace-sim-mzm-pn\"\n",
+    "RF_MESH = {\n",
+    "    \"preset\": \"default\",\n",
+    "    \"refined_mesh_size\": 0.05,\n",
+    "    \"max_mesh_size\": 40.0,\n",
+    "    \"fmax\": 150e9,\n",
+    "}\n",
+    "\n",
+    "# --- RF post-processing -----------------------------------------------------\n",
+    "RF_FIELD = \"E_real\"\n",
+    "RF_FIELD_TITLE = \"RF Mode |E| at x=0 (50 GHz)\"\n",
+    "RIB_PHYSICAL_GROUPS = [\n",
+    "    \"n_rib\",\n",
+    "    \"npp_slab_0\",\n",
+    "    \"npp_slab_1\",\n",
+    "    \"p_rib\",\n",
+    "    \"pp_slab_0\",\n",
+    "    \"pp_slab_1\",\n",
+    "]\n",
+    "\n",
+    "# --- PN junction lumped model -------------------------------------------------\n",
+    "PN_JUNCTION_CAPACITANCE = 1e-15  # F, on the p_rib / n_rib interface"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "12",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "INFO Generating mesh in palace-sim-mzm-pn\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "INFO Extracting geometry...\n",
+      "INFO   Polygons: 17\n",
+      "INFO   Bbox: (-5.0, -70.0, 10.0, 70.0)\n",
+      "INFO Building native 2D BoundaryMode geometry...\n",
+      "INFO Filtered 14 internal conductor curves for 'metal1' (2 remaining)\n",
+      "INFO Filtered 6 internal conductor curves for 'via_contact' (2 remaining)\n",
+      "INFO Generating native 2D BoundaryMode mesh...\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2D domain groups: ['n_rib', 'npp_slab_0', 'npp_slab_1', 'p_rib', 'passive', 'pp_slab_0', 'pp_slab_1', 'sio2', 'slab90', 'air']\n",
+      "  Bounding box: 340.000 x 208.600 x 0.000 um\n",
+      "  Nodes:     42,253\n",
+      "  Elements:  103,726\n",
+      "  Domain groups:     10\n",
+      "  Conductor surfaces:2\n",
+      "  Interface surfaces:17\n",
+      "  Est. ND-space DOFs (order 2):  ~622,356\n",
+      "  Est. H1-space DOFs (order 2):  ~622,356\n",
+      "  Est. total DOFs:                  ~1,244,712\n"
+     ]
+    }
+   ],
+   "source": [
+    "from gsim.palace import BoundaryModeSim\n",
+    "\n",
+    "# -- Boundary 2D simulation setup (RF) ----------------------------------\n",
+    "sim = BoundaryModeSim()\n",
+    "sim.set_output_dir(RF_OUTPUT_DIR)\n",
+    "sim.set_stack(stack)\n",
+    "sim.set_airbox(**AIRBOX)\n",
+    "sim.set_geometry(comp)\n",
+    "\n",
+    "sim.set_cross_section(f\"{CROSS_SECTION_AXIS}={CROSS_SECTION_VALUE}\")\n",
+    "sim.set_boundary_mode(freq=F_RF, num_modes=NUM_RF_MODES, save=2)\n",
+    "\n",
+    "# -- Mesh ---------------------------------------------------------------------\n",
+    "sim.mesh(\n",
+    "    preset=RF_MESH[\"preset\"],\n",
+    "    refined_mesh_size=RF_MESH[\"refined_mesh_size\"],\n",
+    "    max_mesh_size=RF_MESH[\"max_mesh_size\"],\n",
+    "    fmax=RF_MESH[\"fmax\"],\n",
+    "    margin_x=MESH_MARGIN_X,\n",
+    "    margin_y=MESH_MARGIN_Y,\n",
+    ")\n",
+    "\n",
+    "# Show the 2D domain groups created by the solver\n",
+    "domain_groups = list(sim._last_mesh_result.groups[\"volumes\"].keys())\n",
+    "print(\"2D domain groups:\", domain_groups)\n",
+    "sim.print_mesh_stats()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "13",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "INFO Solid plot: using 1 surface cell blocks\n",
+      "INFO awaiting runner setup\n",
+      "INFO awaiting site startup\n",
+      "INFO Print WSLINK_READY_MSG\n",
+      "INFO Schedule auto shutdown with timeout 0\n",
+      "INFO awaiting running future\n"
+     ]
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "b63ec5af348f44efb65c940d2aee74a1",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Widget(value='<iframe src=\"http://localhost:34191/index.html?ui=P_0x75d50ef6fb00_0&reconnect=auto\" class=\"pyvi…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "INFO 127.0.0.1 [10/Aug/2026:17:43:00 -0300] \"GET /index.html?ui=P_0x75d402f5ee70_3&reconnect=auto HTTP/1.1\" 200 237 \"-\" \"Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Code/1.115.0 Chrome/142.0.7444.265 Electron/39.8.5 Safari/537.36\"\n",
+      "INFO 127.0.0.1 [10/Aug/2026:17:43:00 -0300] \"GET /assets/index-DBTNMoYm.js HTTP/1.1\" 200 246 \"http://localhost:34191/index.html?ui=P_0x75d402f5ee70_3&reconnect=auto\" \"Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Code/1.115.0 Chrome/142.0.7444.265 Electron/39.8.5 Safari/537.36\"\n",
+      "INFO 127.0.0.1 [10/Aug/2026:17:43:00 -0300] \"GET /vue.global.js HTTP/1.1\" 200 247 \"http://localhost:34191/index.html?ui=P_0x75d402f5ee70_3&reconnect=auto\" \"Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Code/1.115.0 Chrome/142.0.7444.265 Electron/39.8.5 Safari/537.36\"\n",
+      "INFO 127.0.0.1 [10/Aug/2026:17:43:00 -0300] \"GET /assets/index-faLoIDve.css HTTP/1.1\" 200 235 \"http://localhost:34191/index.html?ui=P_0x75d402f5ee70_3&reconnect=auto\" \"Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Code/1.115.0 Chrome/142.0.7444.265 Electron/39.8.5 Safari/537.36\"\n",
+      "INFO 127.0.0.1 [10/Aug/2026:17:43:00 -0300] \"GET /loading.tpl HTTP/1.1\" 200 252 \"http://localhost:34191/index.html?ui=P_0x75d402f5ee70_3&reconnect=auto\" \"Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Code/1.115.0 Chrome/142.0.7444.265 Electron/39.8.5 Safari/537.36\"\n",
+      "INFO 127.0.0.1 [10/Aug/2026:17:43:00 -0300] \"POST /paraview/ HTTP/1.1\" 405 209 \"http://localhost:34191/index.html?ui=P_0x75d402f5ee70_3&reconnect=auto\" \"Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Code/1.115.0 Chrome/142.0.7444.265 Electron/39.8.5 Safari/537.36\"\n",
+      "INFO client a1b19026dff9472982a5e6b9ba762100 connected\n",
+      "INFO 127.0.0.1 [10/Aug/2026:17:43:00 -0300] \"GET /__trame_vuetify3_3.2.2/vuetify3.css HTTP/1.1\" 200 240 \"http://localhost:34191/index.html?ui=P_0x75d402f5ee70_3&reconnect=auto\" \"Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Code/1.115.0 Chrome/142.0.7444.265 Electron/39.8.5 Safari/537.36\"\n",
+      "INFO 127.0.0.1 [10/Aug/2026:17:43:00 -0300] \"GET /__trame_vuetify3_3.2.2/css/mdi.css HTTP/1.1\" 200 240 \"http://localhost:34191/index.html?ui=P_0x75d402f5ee70_3&reconnect=auto\" \"Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Code/1.115.0 Chrome/142.0.7444.265 Electron/39.8.5 Safari/537.36\"\n",
+      "INFO 127.0.0.1 [10/Aug/2026:17:43:00 -0300] \"GET /__trame_roboto_3.2.2/roboto.css HTTP/1.1\" 200 235 \"http://localhost:34191/index.html?ui=P_0x75d402f5ee70_3&reconnect=auto\" \"Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Code/1.115.0 Chrome/142.0.7444.265 Electron/39.8.5 Safari/537.36\"\n",
+      "INFO 127.0.0.1 [10/Aug/2026:17:43:00 -0300] \"GET /__trame_vtk_2.11.8/trame-vtk.js HTTP/1.1\" 200 249 \"http://localhost:34191/index.html?ui=P_0x75d402f5ee70_3&reconnect=auto\" \"Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Code/1.115.0 Chrome/142.0.7444.265 Electron/39.8.5 Safari/537.36\"\n",
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+      "INFO 127.0.0.1 [10/Aug/2026:17:44:52 -0300] \"GET /index.html?ui=P_0x75d402f91370_1&reconnect=auto HTTP/1.1\" 200 237 \"-\" \"Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Code/1.115.0 Chrome/142.0.7444.265 Electron/39.8.5 Safari/537.36\"\n",
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+      "INFO 127.0.0.1 [10/Aug/2026:17:44:52 -0300] \"POST /paraview/ HTTP/1.1\" 405 209 \"http://localhost:34191/index.html?ui=P_0x75d402f91370_1&reconnect=auto\" \"Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Code/1.115.0 Chrome/142.0.7444.265 Electron/39.8.5 Safari/537.36\"\n",
+      "INFO 127.0.0.1 [10/Aug/2026:17:44:52 -0300] \"POST /paraview/ HTTP/1.1\" 405 209 \"http://localhost:34191/index.html?ui=P_0x75d50ea288c0_2&reconnect=auto\" \"Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Code/1.115.0 Chrome/142.0.7444.265 Electron/39.8.5 Safari/537.36\"\n",
+      "INFO client ebab238816e7452988b7615fcf21233e connected\n",
+      "INFO client 1664dc79deba4e028ad113d5c9e670f7 connected\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Interactive 3D mesh visualisation\n",
+    "sim.plot_mesh(\n",
+    "    transparent_groups=[\"air__None\", \"air__passive\", \"oxide__passive\"],\n",
+    "    style=\"solid\",\n",
+    "    interactive=True,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "14",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Config written to: palace-sim-mzm-pn\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Generate Palace config file (mesh must be present)\n",
+    "sim.add_impedance_boundary(\"p_rib\", \"n_rib\", capacitance=PN_JUNCTION_CAPACITANCE)\n",
+    "sim.write_config()\n",
+    "print(\"Config written to:\", sim.output_dir)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "15",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "INFO Parallel config: 1 MPI rank(s), 8 OpenMP thread(s)\n",
+      "INFO resolve_palace_binary: using palace-toolkit-cpu bundled binary /home/martin/Desktop/gsim/.venv/lib/python3.12/site-packages/palacetoolkit_palace_cpu/bin/palace\n",
+      "INFO Palace binary: /home/martin/Desktop/gsim/.venv/lib/python3.12/site-packages/palacetoolkit_palace_cpu/bin/palace  (source: palace-toolkit-cpu)\n",
+      "INFO >> /usr/bin/mpirun -n 1 /home/martin/Desktop/gsim/.venv/lib/python3.12/site-packages/palacetoolkit_palace_cpu/bin/palace-x86_64.bin --version\n",
+      "\n",
+      "Palace version: v0.17.0-194-g01f5d9bd1\n",
+      "Schema version: 1-3-1\n",
+      "INFO Running Palace simulation in palace-sim-mzm-pn directly\n",
+      "INFO Command: /home/martin/Desktop/gsim/.venv/lib/python3.12/site-packages/palacetoolkit_palace_cpu/bin/palace -np 1 -nt 8 config.json\n",
+      "INFO Processes: 1\n",
+      "INFO >> /usr/bin/mpirun -n 1 /home/martin/Desktop/gsim/.venv/lib/python3.12/site-packages/palacetoolkit_palace_cpu/bin/palace-x86_64.bin config.json\n",
+      "INFO _____________     _______\n",
+      "INFO _____   __   \\____ __   /____ ____________\n",
+      "INFO ____   /_/  /  __ ` /  /  __ ` /  ___/  _ \\\n",
+      "INFO ___   _____/  /_/  /  /  /_/  /  /__/  ___/\n",
+      "INFO   /__/     \\___,__/__/\\___,__/\\_____\\_____/\n",
+      "INFO \u001b[38;2;255;255;000m--> Warning!\u001b[0m\n",
+      "INFO Output folder is not empty; program will overwrite content! (output/palace)\n",
+      "INFO Git changeset ID: v0.17.0-194-g01f5d9bd1\n",
+      "INFO Running with 1 MPI process, 8 OpenMP threads\n",
+      "INFO Device configuration: omp,cpu\n",
+      "INFO Memory configuration: host-std\n",
+      "INFO libCEED backend: /cpu/self/xsmm/blocked\n",
+      "INFO \u001b[38;2;255;255;000m--> Warning!\u001b[0m\n",
+      "INFO One or more external boundary attributes has no associated boundary condition!\n",
+      "INFO \"PMC\"/\"ZeroCharge\" condition is assumed!\n",
+      "INFO Boundary attribute list: 30\n",
+      "INFO \u001b[38;2;255;255;000m--> Warning!\u001b[0m\n",
+      "INFO 5505 mesh faces with no associated boundary element exist on the domain boundary!\n",
+      "INFO Added 9 duplicate vertices for interior boundaries in the mesh\n",
+      "INFO Added 10 duplicate boundary elements for interior boundaries in the mesh\n",
+      "INFO Added 5505 boundary elements for exterior boundaries to the mesh\n",
+      "INFO Characteristic length and time scales:\n",
+      "INFO  Lc = 3.400e-04 m, tc = 1.134e-03 ns\n",
+      "INFO Finished partitioning mesh into 1 subdomain\n",
+      "INFO Mesh curvature order: 1\n",
+      "INFO Mesh bounding box:\n",
+      "INFO  (Xmin, Ymin) = (-1.700e-04, -1.030e-04) m\n",
+      "INFO  (Xmax, Ymax) = (+1.700e-04, +1.056e-04) m\n",
+      "INFO Parallel Mesh Stats:\n",
+      "INFO                 minimum     average     maximum       total\n",
+      "INFO  vertices         37401       37401       37401       37401\n",
+      "INFO  edges           105329      105329      105329      105329\n",
+      "INFO  elements         67925       67925       67925       67925\n",
+      "INFO  neighbors            0           0           0\n",
+      "INFO             minimum     maximum\n",
+      "INFO  h      5.10804e-05    0.127602\n",
+      "INFO  kappa      1.00053     11.0745\n",
+      "INFO Estimated current per-rank memory usage is: Min. 79.8M, Max. 79.8M, Avg. 79.8M, Total 79.8M\n",
+      "INFO Estimated current per-node memory usage is: Min. 79.8M, Max. 79.8M, Avg. 79.8M, Total 79.8M\n",
+      "INFO Configuring 2D waveguide mode analysis at f = 5.000e+01 GHz (omega = 3.562937e-01)\n",
+      "INFO Configuring Robin impedance BC at attributes:\n",
+      "INFO  14: Cs = 4.545e-09 F/sq, n = (+1.0,+0.0)\n",
+      "INFO Configuring Robin finite conductivity BC at attributes:\n",
+      "INFO  11: σ = 3.770e+07 S/m, h = 1.000e-06 m, n = (-0.0,-1.0)\n",
+      "INFO  12: σ = 3.770e+07 S/m, h = 1.010e-06 m, n = (-0.8,+0.6)\n",
+      "INFO  ND space: 346508 DOFs, H1 space: 142730 DOFs, total: 489238\n",
+      "INFO  SuperLUSolver: Using 2D processor grid 1 x 1\n",
+      "INFO  Auto kn_target = 1.289074e+00 (from max(mu_r) * max(epsilon_r) = 1.190000e+01)\n",
+      "INFO Solving GEP for 2 propagation mode(s)...\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO ** Memory Usage **********************************\n",
+      "INFO ** Total highmark (MB):\n",
+      "INFO     Sum-of-all :  1570.68 | Avg :  1570.68  | Max :  1570.68\n",
+      "INFO     Max at rank 0, different stages (MB):\n",
+      "INFO \t. symbfact          194.65\n",
+      "INFO \t. distribution     1570.68\n",
+      "INFO \t. numfact           386.64\n",
+      "INFO ** NUMfact space (MB): (sum-of-all-processes)\n",
+      "INFO     L\\U :          363.33 |  Total :   386.64\n",
+      "INFO \t. max at rank 0, max L+U memory (MB):   363.33\n",
+      "INFO \t. max at rank 0, peak buffer (MB):       23.31\n",
+      "INFO **************************************************\n",
+      "INFO ** number of Tiny Pivots:        0\n",
+      "INFO   0 (restart 0) KSP residual norm 4.311978e-01\n",
+      "INFO   1 (restart 0) KSP residual norm 3.251909e-02\n",
+      "INFO   2 (restart 0) KSP residual norm 3.734024e-03\n",
+      "INFO   3 (restart 0) KSP residual norm 1.274135e-03\n",
+      "INFO   4 (restart 0) KSP residual norm 2.080839e-04\n",
+      "INFO   5 (restart 0) KSP residual norm 6.469820e-05\n",
+      "INFO   6 (restart 0) KSP residual norm 1.348205e-05\n",
+      "INFO   7 (restart 0) KSP residual norm 3.905597e-06\n",
+      "INFO   8 (restart 0) KSP residual norm 8.000766e-07\n",
+      "INFO   9 (restart 0) KSP residual norm 1.992903e-07\n",
+      "INFO GMRES solver converged in 9 iterations (avg. reduction factor: 1.977e-01)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.303786e-01\n",
+      "INFO   1 (restart 0) KSP residual norm 1.527401e-02\n",
+      "INFO   2 (restart 0) KSP residual norm 9.418361e-04\n",
+      "INFO   3 (restart 0) KSP residual norm 2.519848e-04\n",
+      "INFO   4 (restart 0) KSP residual norm 3.944511e-05\n",
+      "INFO   5 (restart 0) KSP residual norm 1.099442e-05\n",
+      "INFO   6 (restart 0) KSP residual norm 1.731546e-06\n",
+      "INFO   7 (restart 0) KSP residual norm 3.814820e-07\n",
+      "INFO   8 (restart 0) KSP residual norm 1.269452e-07\n",
+      "INFO GMRES solver converged in 8 iterations (avg. reduction factor: 1.651e-01)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.917301e-01\n",
+      "INFO   1 (restart 0) KSP residual norm 6.503884e-02\n",
+      "INFO   2 (restart 0) KSP residual norm 3.574316e-03\n",
+      "INFO   3 (restart 0) KSP residual norm 7.715809e-04\n",
+      "INFO   4 (restart 0) KSP residual norm 1.495854e-04\n",
+      "INFO   5 (restart 0) KSP residual norm 4.349322e-05\n",
+      "INFO   6 (restart 0) KSP residual norm 7.304207e-06\n",
+      "INFO   7 (restart 0) KSP residual norm 1.414720e-06\n",
+      "INFO   8 (restart 0) KSP residual norm 4.685188e-07\n",
+      "INFO   9 (restart 0) KSP residual norm 1.119082e-07\n",
+      "INFO GMRES solver converged in 9 iterations (avg. reduction factor: 1.937e-01)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.803317e-01\n",
+      "INFO   1 (restart 0) KSP residual norm 2.610150e-01\n",
+      "INFO   2 (restart 0) KSP residual norm 1.696129e-02\n",
+      "INFO   3 (restart 0) KSP residual norm 5.109055e-03\n",
+      "INFO   4 (restart 0) KSP residual norm 5.247284e-04\n",
+      "INFO   5 (restart 0) KSP residual norm 1.173352e-04\n",
+      "INFO   6 (restart 0) KSP residual norm 1.923893e-05\n",
+      "INFO   7 (restart 0) KSP residual norm 5.627168e-06\n",
+      "INFO   8 (restart 0) KSP residual norm 1.422109e-06\n",
+      "INFO   9 (restart 0) KSP residual norm 3.180880e-07\n",
+      "INFO GMRES solver converged in 9 iterations (avg. reduction factor: 1.924e-01)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.910397e-01\n",
+      "INFO   1 (restart 0) KSP residual norm 2.059546e-01\n",
+      "INFO   2 (restart 0) KSP residual norm 1.303738e-02\n",
+      "INFO   3 (restart 0) KSP residual norm 3.933778e-03\n",
+      "INFO   4 (restart 0) KSP residual norm 3.952494e-04\n",
+      "INFO   5 (restart 0) KSP residual norm 7.839015e-05\n",
+      "INFO   6 (restart 0) KSP residual norm 1.444870e-05\n",
+      "INFO   7 (restart 0) KSP residual norm 4.504327e-06\n",
+      "INFO   8 (restart 0) KSP residual norm 1.018845e-06\n",
+      "INFO   9 (restart 0) KSP residual norm 2.413029e-07\n",
+      "INFO GMRES solver converged in 9 iterations (avg. reduction factor: 1.863e-01)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.999342e-01\n",
+      "INFO   1 (restart 0) KSP residual norm 1.340847e-01\n",
+      "INFO   2 (restart 0) KSP residual norm 8.300592e-03\n",
+      "INFO   3 (restart 0) KSP residual norm 2.617997e-03\n",
+      "INFO   4 (restart 0) KSP residual norm 2.702214e-04\n",
+      "INFO   5 (restart 0) KSP residual norm 5.260457e-05\n",
+      "INFO   6 (restart 0) KSP residual norm 1.097212e-05\n",
+      "INFO   7 (restart 0) KSP residual norm 2.824168e-06\n",
+      "INFO   8 (restart 0) KSP residual norm 6.575297e-07\n",
+      "INFO   9 (restart 0) KSP residual norm 1.647405e-07\n",
+      "INFO GMRES solver converged in 9 iterations (avg. reduction factor: 1.866e-01)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.064810e+00\n",
+      "INFO   1 (restart 0) KSP residual norm 2.676624e-01\n",
+      "INFO   2 (restart 0) KSP residual norm 1.384133e-02\n",
+      "INFO   3 (restart 0) KSP residual norm 4.501028e-03\n",
+      "INFO   4 (restart 0) KSP residual norm 4.732709e-04\n",
+      "INFO   5 (restart 0) KSP residual norm 9.935148e-05\n",
+      "INFO   6 (restart 0) KSP residual norm 1.916464e-05\n",
+      "INFO   7 (restart 0) KSP residual norm 4.946092e-06\n",
+      "INFO   8 (restart 0) KSP residual norm 1.412746e-06\n",
+      "INFO   9 (restart 0) KSP residual norm 3.358504e-07\n",
+      "INFO GMRES solver converged in 9 iterations (avg. reduction factor: 1.895e-01)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.407982e-01\n",
+      "INFO   1 (restart 0) KSP residual norm 1.832969e-01\n",
+      "INFO   2 (restart 0) KSP residual norm 1.258816e-02\n",
+      "INFO   3 (restart 0) KSP residual norm 2.206729e-03\n",
+      "INFO   4 (restart 0) KSP residual norm 2.543534e-04\n",
+      "INFO   5 (restart 0) KSP residual norm 6.598104e-05\n",
+      "INFO   6 (restart 0) KSP residual norm 1.200245e-05\n",
+      "INFO   7 (restart 0) KSP residual norm 3.724339e-06\n",
+      "INFO   8 (restart 0) KSP residual norm 7.965121e-07\n",
+      "INFO GMRES solver converged in 8 iterations (avg. reduction factor: 1.766e-01)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.021860e-01\n",
+      "INFO   1 (restart 0) KSP residual norm 1.082270e-01\n",
+      "INFO   2 (restart 0) KSP residual norm 1.392661e-02\n",
+      "INFO   3 (restart 0) KSP residual norm 3.541033e-03\n",
+      "INFO   4 (restart 0) KSP residual norm 4.434855e-04\n",
+      "INFO   5 (restart 0) KSP residual norm 7.161519e-05\n",
+      "INFO   6 (restart 0) KSP residual norm 1.558321e-05\n",
+      "INFO   7 (restart 0) KSP residual norm 5.031873e-06\n",
+      "INFO   8 (restart 0) KSP residual norm 1.040861e-06\n",
+      "INFO   9 (restart 0) KSP residual norm 2.600300e-07\n",
+      "INFO GMRES solver converged in 9 iterations (avg. reduction factor: 1.901e-01)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.703782e-01\n",
+      "INFO   1 (restart 0) KSP residual norm 1.416725e-01\n",
+      "INFO   2 (restart 0) KSP residual norm 8.873686e-03\n",
+      "INFO   3 (restart 0) KSP residual norm 2.930851e-03\n",
+      "INFO   4 (restart 0) KSP residual norm 2.386510e-04\n",
+      "INFO   5 (restart 0) KSP residual norm 4.448407e-05\n",
+      "INFO   6 (restart 0) KSP residual norm 9.502781e-06\n",
+      "INFO   7 (restart 0) KSP residual norm 3.031567e-06\n",
+      "INFO   8 (restart 0) KSP residual norm 5.944656e-07\n",
+      "INFO GMRES solver converged in 8 iterations (avg. reduction factor: 1.752e-01)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.367850e+00\n",
+      "INFO   1 (restart 0) KSP residual norm 1.542074e-01\n",
+      "INFO   2 (restart 0) KSP residual norm 1.327399e-02\n",
+      "INFO   3 (restart 0) KSP residual norm 7.157748e-03\n",
+      "INFO   4 (restart 0) KSP residual norm 7.194257e-04\n",
+      "INFO   5 (restart 0) KSP residual norm 1.103927e-04\n",
+      "INFO   6 (restart 0) KSP residual norm 1.870972e-05\n",
+      "INFO   7 (restart 0) KSP residual norm 5.071168e-06\n",
+      "INFO   8 (restart 0) KSP residual norm 1.455129e-06\n",
+      "INFO   9 (restart 0) KSP residual norm 3.837524e-07\n",
+      "INFO GMRES solver converged in 9 iterations (avg. reduction factor: 1.871e-01)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.218116e-01\n",
+      "INFO   1 (restart 0) KSP residual norm 1.627266e-01\n",
+      "INFO   2 (restart 0) KSP residual norm 1.192672e-02\n",
+      "INFO   3 (restart 0) KSP residual norm 6.197981e-03\n",
+      "INFO   4 (restart 0) KSP residual norm 3.049470e-04\n",
+      "INFO   5 (restart 0) KSP residual norm 5.774807e-05\n",
+      "INFO   6 (restart 0) KSP residual norm 1.311698e-05\n",
+      "INFO   7 (restart 0) KSP residual norm 3.794207e-06\n",
+      "INFO   8 (restart 0) KSP residual norm 9.262794e-07\n",
+      "INFO   9 (restart 0) KSP residual norm 2.195738e-07\n",
+      "INFO GMRES solver converged in 9 iterations (avg. reduction factor: 1.861e-01)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.298839e+00\n",
+      "INFO   1 (restart 0) KSP residual norm 1.763912e-01\n",
+      "INFO   2 (restart 0) KSP residual norm 1.279017e-02\n",
+      "INFO   3 (restart 0) KSP residual norm 4.078349e-03\n",
+      "INFO   4 (restart 0) KSP residual norm 4.776859e-04\n",
+      "INFO   5 (restart 0) KSP residual norm 1.041072e-04\n",
+      "INFO   6 (restart 0) KSP residual norm 1.807102e-05\n",
+      "INFO   7 (restart 0) KSP residual norm 4.277864e-06\n",
+      "INFO   8 (restart 0) KSP residual norm 1.332692e-06\n",
+      "INFO   9 (restart 0) KSP residual norm 3.723235e-07\n",
+      "INFO GMRES solver converged in 9 iterations (avg. reduction factor: 1.875e-01)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.939154e-01\n",
+      "INFO   1 (restart 0) KSP residual norm 1.051377e-01\n",
+      "INFO   2 (restart 0) KSP residual norm 9.014619e-03\n",
+      "INFO   3 (restart 0) KSP residual norm 1.645630e-03\n",
+      "INFO   4 (restart 0) KSP residual norm 1.691229e-04\n",
+      "INFO   5 (restart 0) KSP residual norm 5.413641e-05\n",
+      "INFO   6 (restart 0) KSP residual norm 6.429066e-06\n",
+      "INFO   7 (restart 0) KSP residual norm 2.321035e-06\n",
+      "INFO   8 (restart 0) KSP residual norm 5.904709e-07\n",
+      "INFO GMRES solver converged in 8 iterations (avg. reduction factor: 1.743e-01)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.097956e-01\n",
+      "INFO   1 (restart 0) KSP residual norm 1.061979e-01\n",
+      "INFO   2 (restart 0) KSP residual norm 8.535180e-03\n",
+      "INFO   3 (restart 0) KSP residual norm 2.975140e-03\n",
+      "INFO   4 (restart 0) KSP residual norm 2.318686e-04\n",
+      "INFO   5 (restart 0) KSP residual norm 6.278673e-05\n",
+      "INFO   6 (restart 0) KSP residual norm 9.191402e-06\n",
+      "INFO   7 (restart 0) KSP residual norm 2.802139e-06\n",
+      "INFO   8 (restart 0) KSP residual norm 6.924306e-07\n",
+      "INFO GMRES solver converged in 8 iterations (avg. reduction factor: 1.744e-01)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.063137e+00\n",
+      "INFO   1 (restart 0) KSP residual norm 2.706339e-01\n",
+      "INFO   2 (restart 0) KSP residual norm 1.700256e-02\n",
+      "INFO   3 (restart 0) KSP residual norm 3.098561e-03\n",
+      "INFO   4 (restart 0) KSP residual norm 2.703953e-04\n",
+      "INFO   5 (restart 0) KSP residual norm 8.432331e-05\n",
+      "INFO   6 (restart 0) KSP residual norm 1.263736e-05\n",
+      "INFO   7 (restart 0) KSP residual norm 4.951224e-06\n",
+      "INFO   8 (restart 0) KSP residual norm 9.558571e-07\n",
+      "INFO GMRES solver converged in 8 iterations (avg. reduction factor: 1.755e-01)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.727854e-01\n",
+      "INFO   1 (restart 0) KSP residual norm 1.144219e-01\n",
+      "INFO   2 (restart 0) KSP residual norm 1.040829e-02\n",
+      "INFO   3 (restart 0) KSP residual norm 2.504828e-03\n",
+      "INFO   4 (restart 0) KSP residual norm 2.027984e-04\n",
+      "INFO   5 (restart 0) KSP residual norm 6.398187e-05\n",
+      "INFO   6 (restart 0) KSP residual norm 8.390295e-06\n",
+      "INFO   7 (restart 0) KSP residual norm 2.700902e-06\n",
+      "INFO   8 (restart 0) KSP residual norm 6.636951e-07\n",
+      "INFO GMRES solver converged in 8 iterations (avg. reduction factor: 1.745e-01)\n",
+      "INFO  Found 7 converged eigenvalues (sigma = -1.661712e+00)\n",
+      "INFO  eig 0: kn = 6.691632e-01-2.817020e-02i, n_eff = 1.878123e+00-7.906456e-02i\n",
+      "INFO  eig 1: kn = 5.189958e-01-4.367772e-03i, n_eff = 1.456652e+00-1.225891e-02i\n",
+      "INFO  eig 2: kn = 4.930991e-01-1.118367e-03i, n_eff = 1.383968e+00-3.138890e-03i\n",
+      "INFO  eig 3: kn = 4.320170e-01-3.258113e-03i, n_eff = 1.212531e+00-9.144461e-03i\n",
+      "INFO  eig 4: kn = 3.921596e-01-3.884368e-04i, n_eff = 1.100664e+00-1.090215e-03i\n",
+      "INFO  eig 5: kn = 2.591523e-04-2.593977e+00i, n_eff = 7.273559e-04-7.280448e+00i\n",
+      "INFO  eig 6: kn = 1.299908e-04-3.628987e+00i, n_eff = 3.648419e-04-1.018538e+01i\n",
+      "INFO Computing solution error estimates and performing postprocessing\n",
+      "INFO      m,       Re{kn} (1/m),       Im{kn} (1/m),          Re{n_eff},          Im{n_eff},      Error (Bkwd.),       Error (Abs.)\n",
+      "INFO      1,      +1.968127e+03,      -8.285353e+01,      +1.878123e+00,      -7.906456e-02,      +1.473479e-16,      +7.846959e-07\n",
+      "INFO  Wrote mode 1 to disk (Paraview)\n",
+      "INFO      2,      +1.526458e+03,      -1.284639e+01,      +1.456652e+00,      -1.225891e-02,      +4.474098e-16,      +2.079659e-06\n",
+      "INFO  Wrote mode 2 to disk (Paraview)\n",
+      "INFO Completed 0 iterations of adaptive mesh refinement (AMR):\n",
+      "INFO  Indicator norm = 1.013e-01, global unknowns = 489238\n",
+      "INFO  Max. iterations = 0, tol. = 1.000e-02\n",
+      "INFO Estimated peak per-rank memory usage is: Min. 2.7G, Max. 2.7G, Avg. 2.7G, Total 2.7G\n",
+      "INFO Estimated peak per-node memory usage is: Min. 2.7G, Max. 2.7G, Avg. 2.7G, Total 2.7G\n",
+      "INFO Elapsed Time Report (s)           Min.        Max.        Avg.\n",
+      "INFO ==============================================================\n",
+      "INFO Initialization                   0.109       0.109       0.109\n",
+      "INFO   Mesh Preprocessing             0.365       0.365       0.365\n",
+      "INFO Operator Construction            1.155       1.155       1.155\n",
+      "INFO   Preconditioner                63.139      63.139      63.139\n",
+      "INFO Eigenvalue Solve                11.655      11.655      11.655\n",
+      "INFO Estimation                       0.102       0.102       0.102\n",
+      "INFO   Construction                  17.333      17.333      17.333\n",
+      "INFO   Solve                          5.458       5.458       5.458\n",
+      "INFO Postprocessing                  17.121      17.121      17.121\n",
+      "INFO   Paraview                      10.311      10.311      10.311\n",
+      "INFO Disk IO                          0.168       0.168       0.168\n",
+      "INFO --------------------------------------------------------------\n",
+      "INFO Total                          127.153     127.153     127.153\n",
+      "INFO Peak Memory                   Per-Node       Total   Total HWM\n",
+      "INFO ==============================================================\n",
+      "INFO Initialization                    4.3M        4.3M        4.3M\n",
+      "INFO   Mesh Preprocessing             31.3M       31.3M       35.6M\n",
+      "INFO Operator Construction           542.8M      542.8M      578.4M\n",
+      "INFO   Preconditioner                  1.5G        1.5G        2.1G\n",
+      "INFO Eigenvalue Solve                516.3M      516.3M        2.6G\n",
+      "INFO Estimation                        0.0K        0.0K        2.6G\n",
+      "INFO   Construction                   42.1M       42.1M        2.7G\n",
+      "INFO   Solve                           0.0K        0.0K        2.7G\n",
+      "INFO Postprocessing                    0.0K        0.0K        2.7G\n",
+      "INFO   Paraview                        0.0K        0.0K        2.7G\n",
+      "INFO Disk IO                          17.4M       17.4M        2.7G\n",
+      "INFO --------------------------------------------------------------\n",
+      "INFO Total                             2.7G        2.7G        2.7G\n",
+      "INFO Simulation completed successfully\n",
+      "INFO Results saved to palace-sim-mzm-pn/output/palace\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "mode 1: k_n = +1.968127e+03-8.285353e+01j, n_eff = +1.878123e+00-7.906456e-02j, eta_eff ~= 200.23+8.43j\n",
+      "mode 2: k_n = +1.526458e+03-1.284639e+01j, n_eff = +1.456652e+00-1.225891e-02j, eta_eff ~= 258.61+2.18j\n"
+     ]
+    }
+   ],
+   "source": [
+    "# -- RF simulation (50 GHz) ------------------------------------------------\n",
+    "results = sim.run_local(verbose=True)\n",
+    "results.print()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "16",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "mode 1: k_n = +1.968127e+03-8.285353e+01j, n_eff = +1.878123e+00-7.906456e-02j, eta_eff ~= 200.23+8.43j\n",
+      "mode 2: k_n = +1.526458e+03-1.284639e+01j, n_eff = +1.456652e+00-1.225891e-02j, eta_eff ~= 258.61+2.18j\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "INFO Input field is already 2D in z-normal plane; ignoring normal=x\n"
+     ]
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "b1acc72082804e79872c08e993c295a6",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Widget(value='<iframe src=\"http://localhost:34191/index.html?ui=P_0x75d402f91370_1&reconnect=auto\" class=\"pyvi…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# --- Post-processing: RF mode fields ---\n",
+    "import importlib\n",
+    "\n",
+    "import gsim.palace.field_viz as field_viz\n",
+    "import gsim.palace.results as palace_results\n",
+    "from gsim.palace import plot_fields_2d\n",
+    "\n",
+    "importlib.reload(field_viz)\n",
+    "importlib.reload(palace_results)\n",
+    "\n",
+    "if not hasattr(results, \"modes\"):\n",
+    "    results = palace_results.load_text_results(RF_OUTPUT_DIR)\n",
+    "\n",
+    "results.print()\n",
+    "\n",
+    "pl = plot_fields_2d(\n",
+    "    RF_OUTPUT_DIR,\n",
+    "    field=RF_FIELD,\n",
+    "    title=RF_FIELD_TITLE,\n",
+    "    interactive=True,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "17",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "INFO Selected 1172 / 67925 cells for physical_groups=['n_rib', 'npp_slab_0', 'npp_slab_1', 'p_rib', 'pp_slab_0', 'pp_slab_1']\n",
+      "INFO Input field is already 2D in z-normal plane; ignoring normal=x\n"
+     ]
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "fcddc777d61b4b0e895f564bde99749c",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Widget(value='<iframe src=\"http://localhost:34191/index.html?ui=P_0x75d50ea288c0_2&reconnect=auto\" class=\"pyvi…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# --- Rib waveguide zoom: select by physical group names ---\n",
+    "from gsim.palace import plot_fields_2d\n",
+    "\n",
+    "pl = plot_fields_2d(\n",
+    "    RF_OUTPUT_DIR,\n",
+    "    field=RF_FIELD,\n",
+    "    physical_groups=RIB_PHYSICAL_GROUPS,\n",
+    "    title=\"RF Mode |E| in the Rib Waveguide (50 GHz, zoomed)\",\n",
+    "    interactive=True,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "18",
+   "metadata": {},
+   "source": [
+    "## Optical simulation (1550 nm)\n",
+    "\n",
+    "The **simplified optical component** (rib + slab + PN junction, all Si) is\n",
+    "analysed at optical frequencies to compute the mode confined in the rib\n",
+    "waveguide. It uses the minimal all-dielectric stack with a **uniform SiO2\n",
+    "cladding** and **no air**: the padded 2D domain background is set to SiO2 via\n",
+    "`set_airbox(material=\"sio2\", ...)` instead of the default air.\n",
+    "`run_local()` locates the Palace binary internally — there is no\n",
+    "manual `subprocess` / binary-search here.\n",
+    "\n",
+    "Material dispersion is evaluated at `F_OPT` by the boundary-mode config\n",
+    "generator, so the Si and SiO2 domains use their Sellmeier optical constants."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "19",
+   "metadata": {
+    "lines_to_next_cell": 2
+   },
+   "outputs": [],
+   "source": [
+    "# =============================================================================\n",
+    "#  Optical parameters (1550 nm BoundaryMode run)\n",
+    "# =============================================================================\n",
+    "\n",
+    "F_OPT = 193.4e12  # ~1550 nm\n",
+    "LAMBDA_OPT = 1.55  # reference wavelength (um)\n",
+    "NUM_OPT_MODES = 4\n",
+    "TARGET_INDEX = 2.5\n",
+    "TOLERANCE = 1e-8\n",
+    "OPT_OUTPUT_DIR = \"./palace-sim-mzm-pn-opt\"\n",
+    "OPT_MESH = {\n",
+    "    \"preset\": \"default\",\n",
+    "    \"refined_mesh_size\": 0.2,\n",
+    "    \"max_mesh_size\": 0.5,\n",
+    "}\n",
+    "\n",
+    "# Optical post-processing\n",
+    "OPT_FIELD = \"E_real\"\n",
+    "OPT_FIELD_TITLE = \"Optical Mode |E| at x=0 (1550 nm)\"\n",
+    "OPT_RIB_PHYSICAL_GROUPS = [\"slab\", \"p_rib\", \"n_rib\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "20",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "INFO Generating mesh in palace-sim-mzm-pn-opt\n",
+      "INFO Extracting geometry...\n",
+      "INFO   Polygons: 4\n",
+      "INFO   Bbox: (-5.0, -50.2, 10.0, 50.2)\n",
+      "INFO Building native 2D BoundaryMode geometry...\n",
+      "INFO Generating native 2D BoundaryMode mesh...\n",
+      "WARNING Absorbing boundary is applied to solid dielectric surfaces (n_rib, p_rib, sio2, slab) because the model has no air region, which produces large spurious insertion loss and reflection. Add an airbox via set_airbox(margin_x=..., margin_y=..., z_above=..., z_below=...). Note that get_stack(air_above=...) is deprecated and ignored.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "PosixPath('palace-sim-mzm-pn-opt/config.json')"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# -- Optical setup + run (1550 nm) ---------------------------------------\n",
+    "sim_optical = BoundaryModeSim()\n",
+    "sim_optical.set_output_dir(OPT_OUTPUT_DIR)\n",
+    "sim_optical.set_stack(stack_opt)\n",
+    "# Uniform SiO2 cladding: the padded 2D domain is filled with SiO2 (material=\n",
+    "# \"sio2\") instead of air, so the device sits in a uniform dielectric background.\n",
+    "# Only modest padding is needed since the cladding now surrounds the rib\n",
+    "# directly. The \"absorbing boundary on solid dielectric\" warning from mesh() is\n",
+    "# expected here — for an eigenmode cross-section the PML sits far from the mode.\n",
+    "sim_optical.set_airbox(\n",
+    "    material=\"sio2\",\n",
+    "    margin_x=3.0,\n",
+    "    margin_y=3.0,\n",
+    "    z_above=3.0,\n",
+    "    z_below=2.0,\n",
+    ")\n",
+    "sim_optical.set_geometry(comp_optical)\n",
+    "\n",
+    "sim_optical.set_cross_section(f\"{CROSS_SECTION_AXIS}={CROSS_SECTION_VALUE}\")\n",
+    "sim_optical.set_boundary_mode(\n",
+    "    freq=F_OPT,\n",
+    "    num_modes=NUM_OPT_MODES,\n",
+    "    save=2,\n",
+    "    target=TARGET_INDEX,\n",
+    "    tolerance=TOLERANCE,\n",
+    ")\n",
+    "\n",
+    "# Optical constants at 1550 nm (Sellmeier). The config generator also resolves\n",
+    "# dispersion at F_OPT automatically; these overrides keep the config explicit.\n",
+    "sim_optical.set_material(\n",
+    "    \"si\", material_type=\"dielectric\", permittivity=si_opt.permittivity_scalar\n",
+    ")\n",
+    "sim_optical.set_material(\n",
+    "    \"sio2\", material_type=\"dielectric\", permittivity=sio2_opt.permittivity_scalar\n",
+    ")\n",
+    "\n",
+    "sim_optical.mesh(\n",
+    "    preset=OPT_MESH[\"preset\"],\n",
+    "    refined_mesh_size=OPT_MESH[\"refined_mesh_size\"],\n",
+    "    max_mesh_size=OPT_MESH[\"max_mesh_size\"],\n",
+    ")\n",
+    "\n",
+    "# The optical-only stack has no conductors (only shaped dielectrics), which the\n",
+    "# default write_config() mesh validation accepts. Generate config.json so the\n",
+    "# local run below has something to submit.\n",
+    "sim_optical.write_config()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "21",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "INFO Solid plot: using 1 surface cell blocks\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "c56b0705383a4d75831fb7e48ade6eb4",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Widget(value='<iframe src=\"http://localhost:34191/index.html?ui=P_0x75d402f5ee70_3&reconnect=auto\" class=\"pyvi…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Interactive 3D mesh visualisation\n",
+    "sim_optical.plot_mesh(\n",
+    "    transparent_groups=[\"air__None\", \"air__passive\", \"oxide__passive\"],\n",
+    "    style=\"solid\",\n",
+    "    interactive=True,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "22",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "INFO Parallel config: 1 MPI rank(s), 8 OpenMP thread(s)\n",
+      "INFO resolve_palace_binary: using palace-toolkit-cpu bundled binary /home/martin/Desktop/gsim/.venv/lib/python3.12/site-packages/palacetoolkit_palace_cpu/bin/palace\n",
+      "INFO Palace binary: /home/martin/Desktop/gsim/.venv/lib/python3.12/site-packages/palacetoolkit_palace_cpu/bin/palace  (source: palace-toolkit-cpu)\n",
+      "INFO >> /usr/bin/mpirun -n 1 /home/martin/Desktop/gsim/.venv/lib/python3.12/site-packages/palacetoolkit_palace_cpu/bin/palace-x86_64.bin --version\n",
+      "\n",
+      "Palace version: v0.17.0-194-g01f5d9bd1\n",
+      "Schema version: 1-3-1\n",
+      "INFO Running Palace simulation in palace-sim-mzm-pn-opt directly\n",
+      "INFO Command: /home/martin/Desktop/gsim/.venv/lib/python3.12/site-packages/palacetoolkit_palace_cpu/bin/palace -np 1 -nt 8 config.json\n",
+      "INFO Processes: 1\n",
+      "INFO >> /usr/bin/mpirun -n 1 /home/martin/Desktop/gsim/.venv/lib/python3.12/site-packages/palacetoolkit_palace_cpu/bin/palace-x86_64.bin config.json\n",
+      "INFO _____________     _______\n",
+      "INFO _____   __   \\____ __   /____ ____________\n",
+      "INFO ____   /_/  /  __ ` /  /  __ ` /  ___/  _ \\\n",
+      "INFO ___   _____/  /_/  /  /  /_/  /  /__/  ___/\n",
+      "INFO   /__/     \\___,__/__/\\___,__/\\_____\\_____/\n",
+      "INFO \u001b[38;2;255;255;000m--> Warning!\u001b[0m\n",
+      "INFO Output folder is not empty; program will overwrite content! (output/palace)\n",
+      "INFO Git changeset ID: v0.17.0-194-g01f5d9bd1\n",
+      "INFO Running with 1 MPI process, 8 OpenMP threads\n",
+      "INFO Device configuration: omp,cpu\n",
+      "INFO Memory configuration: host-std\n",
+      "INFO libCEED backend: /cpu/self/xsmm/blocked\n",
+      "INFO \u001b[38;2;255;255;000m--> Warning!\u001b[0m\n",
+      "INFO One or more external boundary attributes has no associated boundary condition!\n",
+      "INFO \"PMC\"/\"ZeroCharge\" condition is assumed!\n",
+      "INFO Boundary attribute list: 11\n",
+      "INFO Characteristic length and time scales:\n",
+      "INFO  Lc = 1.124e-04 m, tc = 3.749e-04 ns\n",
+      "INFO Finished partitioning mesh into 1 subdomain\n",
+      "INFO Mesh curvature order: 1\n",
+      "INFO Mesh bounding box:\n",
+      "INFO  (Xmin, Ymin) = (-5.620e-05, -4.000e-06) m\n",
+      "INFO  (Xmax, Ymax) = (+5.620e-05, +6.000e-06) m\n",
+      "INFO Parallel Mesh Stats:\n",
+      "INFO                 minimum     average     maximum       total\n",
+      "INFO  vertices         12128       12128       12128       12128\n",
+      "INFO  edges            35891       35891       35891       35891\n",
+      "INFO  elements         23764       23764       23764       23764\n",
+      "INFO  neighbors            0           0           0\n",
+      "INFO             minimum     maximum\n",
+      "INFO  h       0.00064132  0.00581142\n",
+      "INFO  kappa      1.00175     3.54786\n",
+      "INFO Estimated current per-rank memory usage is: Min. 54.8M, Max. 54.8M, Avg. 54.8M, Total 54.8M\n",
+      "INFO Estimated current per-node memory usage is: Min. 54.8M, Max. 54.8M, Avg. 54.8M, Total 54.8M\n",
+      "INFO Configuring 2D waveguide mode analysis at f = 1.934e+05 GHz (omega = 4.555981e+02)\n",
+      "INFO  ND space: 119310 DOFs, H1 space: 48019 DOFs, total: 167329\n",
+      "INFO  SuperLUSolver: Using 2D processor grid 1 x 1\n",
+      "INFO  Target n_eff = 2.500000e+00, kn_target = 1.138995e+03\n",
+      "INFO Solving GEP for 4 propagation mode(s)...\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO ** Memory Usage **********************************\n",
+      "INFO ** Total highmark (MB):\n",
+      "INFO     Sum-of-all :   562.47 | Avg :   562.47  | Max :   562.47\n",
+      "INFO     Max at rank 0, different stages (MB):\n",
+      "INFO \t. symbfact           69.62\n",
+      "INFO \t. distribution      562.47\n",
+      "INFO \t. numfact           162.47\n",
+      "INFO ** NUMfact space (MB): (sum-of-all-processes)\n",
+      "INFO     L\\U :          143.23 |  Total :   162.47\n",
+      "INFO \t. max at rank 0, max L+U memory (MB):   143.23\n",
+      "INFO \t. max at rank 0, peak buffer (MB):       19.24\n",
+      "INFO **************************************************\n",
+      "INFO ** number of Tiny Pivots:        0\n",
+      "INFO   0 (restart 0) KSP residual norm 1.197367e-01\n",
+      "INFO   1 (restart 0) KSP residual norm 3.488343e-14\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.913e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.497179e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 2.608407e-15\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.479e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.261750e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 4.955586e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.928e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.211856e-02\n",
+      "INFO   1 (restart 0) KSP residual norm 4.035179e-15\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.330e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.866154e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 1.779723e-15\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.034e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.541508e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 2.393070e-15\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.173e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.980827e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 2.291700e-15\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.283e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.491122e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 1.943699e-15\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.540e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.983151e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 2.685659e-15\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.990e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.162843e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 4.168495e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.585e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.727481e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 2.004375e-15\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.500e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.577711e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 8.717421e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.382e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.645316e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 1.334131e-15\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.660e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.111969e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 6.999299e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.314e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.124666e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 1.444052e-15\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.501e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.074462e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 1.354144e-15\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.323e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.388445e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 1.938279e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.034e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.770195e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 5.503682e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.109e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.869120e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 6.086845e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.257e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.694800e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 1.946181e-15\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.417e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.994004e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 9.489836e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.170e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.095644e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 3.621268e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.305e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.178944e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 8.040074e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.690e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.194083e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 1.199314e-15\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.755e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.596708e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 5.573471e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.491e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.783105e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 5.535886e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.105e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.338105e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 7.166318e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.065e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.043961e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 3.287234e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.149e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.335865e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 7.398614e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.167e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.796602e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.259629e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.325e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.330829e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 8.067183e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.461e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.481112e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 1.902333e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.471e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.051232e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 2.989004e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.302e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.006039e-03\n",
+      "INFO   1 (restart 0) KSP residual norm 3.326314e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.306e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.069157e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 2.452233e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.469e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.469357e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.450419e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.281e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.268945e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 1.944099e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.101e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.284293e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 2.693468e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.901e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.785712e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.086235e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.899e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.777006e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.898369e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.302e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.768122e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 6.353664e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.593e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.927381e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 9.874056e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.373e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.319686e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 1.101116e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.317e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.153844e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 9.807240e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.110e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.266256e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 4.458139e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.521e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.909110e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 5.847159e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.063e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.857829e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 2.722907e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.074e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.066130e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 7.186194e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.478e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.935188e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.788014e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.013e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.352363e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 5.207005e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.850e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.149120e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 7.609307e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.541e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.941741e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 1.129208e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.839e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.511229e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 1.177218e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.353e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.456520e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 1.182102e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.420e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.676602e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 9.272807e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.464e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.806637e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 2.128869e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.128e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.629431e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 5.816911e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.570e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.858267e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.233027e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.196e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.493119e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.787193e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.720e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.030375e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 3.499380e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.396e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.302141e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 3.897459e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.993e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.206691e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 3.949519e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.273e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.842582e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.146708e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.137e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.638915e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.166102e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.205e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.113703e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 1.917795e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.137e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.337656e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 3.848239e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.877e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.175328e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 9.183377e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.892e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.000864e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.192251e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.131e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.093623e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 3.333840e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.048e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.684229e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 5.244659e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.114e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.066270e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 6.505880e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.149e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.680836e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 8.513935e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.176e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.806892e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 9.205170e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.279e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.305559e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 1.719009e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.240e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.106281e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 3.833261e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.465e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.265757e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 6.738407e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.974e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.476332e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.400620e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.129e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.324776e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.979388e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.130e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.004625e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 3.009163e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.342e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.021057e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 3.141429e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.077e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.218815e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 4.290026e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.520e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.249305e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 3.593848e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.877e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.046126e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 2.050287e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.910e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.072431e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 4.259853e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.972e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.283525e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 7.417210e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.248e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.926523e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.403672e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.849e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.443674e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.752711e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.698e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.145346e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 3.664743e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.200e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.465284e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 4.612751e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.148e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.046754e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 6.157487e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.008e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.493943e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 7.990299e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.204e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.556115e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 1.554684e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.412e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.067376e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.793732e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.184e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.813108e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 6.656696e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.671e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.598635e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.234273e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.430e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.856214e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.484846e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.058e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.716830e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.162915e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.220e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.754647e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.566402e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.310e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.610816e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 3.311254e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.445e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.898082e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 3.783459e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.822e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.838399e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 2.080478e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.563e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.291684e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.383741e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.718e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.982563e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 7.220848e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.642e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.250911e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.338257e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.148e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.132975e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.289332e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.733e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.922741e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.839880e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.183e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.075715e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 3.357742e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.121e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.402122e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 5.110974e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.645e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.547382e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 5.071121e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.277e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.807337e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 1.210391e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.179e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.531273e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.858826e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.124e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.416398e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 4.910484e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.467e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.777261e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 9.729200e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.503e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.646012e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.143533e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.136e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.788288e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.528852e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.193e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.223393e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.682716e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.221e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.257207e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.257202e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.607e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.248726e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.278666e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.647e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.558807e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 1.337497e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.934e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.032029e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.543473e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.412e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.830861e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 6.520040e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.561e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.924901e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.329672e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.388e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.308604e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.615420e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.043e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.020078e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.435818e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.470e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.830593e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.760947e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.526e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.622885e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 3.098537e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.220e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.025598e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 3.497491e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.410e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.278918e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 1.112716e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.394e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.982927e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.284368e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.135e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.231451e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 4.663459e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.787e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.314987e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 8.815576e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.808e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.851363e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.053127e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.693e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.581732e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.262099e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.524e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.018997e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.361524e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.388e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.107704e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.986761e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.890e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.476916e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.159130e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.942e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.531054e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 1.168486e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.309e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.577915e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.651190e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.138e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.561163e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 6.135171e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.930e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.090769e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.155639e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.739e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.799086e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.546789e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.071e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.825365e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.823882e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.780e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.496814e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.946252e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.541e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.856046e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.185847e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.188e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.227079e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.566648e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.551e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.826019e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 8.485717e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.003e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.811163e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.117126e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.806e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.068444e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 5.176810e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.845e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.041964e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 8.306133e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.068e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.546912e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 8.995097e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.532e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.328303e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.229699e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.695e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.892048e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.374847e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.532e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.829513e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.723817e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.569e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.022221e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.866499e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.716e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.867492e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 9.363920e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.266e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.493294e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.675020e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.740e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.356140e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 5.721262e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.219e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.594751e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 9.699025e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.738e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.989812e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.053594e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.524e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.537892e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.348285e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.811e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.757140e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.308697e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.483e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.277835e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.414424e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.306e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.104224e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.387850e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.382e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.549679e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 8.502634e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.335e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.269784e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.198308e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 9.864e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.437023e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.650847e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.928e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.736280e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 6.951946e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.004e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.039498e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 7.410028e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.633e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.542374e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.007509e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.963e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.855061e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.014082e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.552e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.378639e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.219177e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.608e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.449869e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.168749e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.388e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.387986e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 7.674674e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.214e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.398754e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.948540e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 9.166e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.161581e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 4.795741e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.129e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.147202e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 7.909144e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.683e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.357816e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 8.871054e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.762e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.697460e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 8.825104e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.272e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.856182e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 9.437870e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.304e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.218496e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.067369e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.316e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.073227e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.219503e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.968e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.230609e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 7.089409e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.178e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.040501e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.624826e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.001e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.158873e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 4.053830e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.498e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.331134e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 7.840961e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.364e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.090176e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 9.776143e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.164e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.337405e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.687553e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.891e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.419764e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.631041e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.009e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.234599e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.530350e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.498e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.573132e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.868244e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.346e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.366943e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 8.079292e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.413e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.594384e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.434215e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.579e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.946341e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 6.090863e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.129e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.933271e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.240494e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.154e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.043655e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.785837e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.541e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.672900e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.180508e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.268e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.162921e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.975692e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.645e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.211571e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 3.879500e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.202e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.848607e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 5.814945e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.146e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.532966e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 7.563801e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.986e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.280665e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.636877e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.622e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.168258e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 3.682787e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.152e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.057082e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 6.843667e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.327e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.532978e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 8.578112e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.387e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.352813e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 9.804615e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.924e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.131501e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.329016e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.217e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.027731e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.031012e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.369e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.389936e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.837231e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.382e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.234704e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 7.033223e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.147e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.007699e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.030354e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.380e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.148890e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 3.583012e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.119e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.112981e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 6.645380e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.145e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.424151e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 7.766703e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.204e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.914217e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 8.352959e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.866e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.084426e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 9.583122e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.107e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.527906e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.010439e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.864e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.636403e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.149151e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.160e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.520026e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 1.148324e-16\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.262e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.757487e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.406192e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.956e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.019261e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.284160e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.254e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.225509e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 5.330885e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.350e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.494066e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 6.249479e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.183e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.060321e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 6.877418e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.338e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.680085e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 9.577096e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.573e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.605708e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.211474e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.360e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.227839e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.609177e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.806e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.027408e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 7.057049e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.481e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.287636e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.347706e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.143e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.733661e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.733809e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.130e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.509922e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 5.693684e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.771e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.545242e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 5.383825e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.484e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.723217e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 5.883705e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.414e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.897880e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 6.094923e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.211e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.315632e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 7.160843e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.092e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.514515e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 8.762991e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.485e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.970403e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 9.898504e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.332e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.031446e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.515724e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.760e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.743435e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.801359e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.618e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.510029e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 5.596319e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.706e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.959699e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 6.895867e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.519e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.806112e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 9.693159e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.454e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.792579e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.199632e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.163e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.118472e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.694290e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.310e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.891166e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.222199e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.772e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.415459e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 5.030927e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.554e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.628377e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.432430e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.948e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.472807e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.759697e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.693e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.224670e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 4.801831e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.921e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.151328e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 4.283772e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.721e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.203099e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 3.913366e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.253e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.277532e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 4.364868e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.417e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.500666e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 5.648276e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.764e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.516729e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 5.669169e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.738e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.383229e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 7.948118e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.335e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.484186e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.851048e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.313e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.589268e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.105754e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.616e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.736552e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 7.007854e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.035e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.261452e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 8.364977e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.699e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.184797e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.015190e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.188e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.145158e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.513494e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.651e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.332286e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.091491e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.922e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.864771e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.806935e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.081e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.626463e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 2.885717e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.998e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.694861e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.626280e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.035e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.583979e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.521563e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.830e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.047323e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 4.712870e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.500e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.314121e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.936446e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.226e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.231347e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.541946e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.837e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.935091e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.522300e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.942e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.700775e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.587275e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.698e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.035896e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.230917e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.576e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.926688e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 6.218473e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.228e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.788674e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.095103e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.513e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.925260e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.269984e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.664e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.819490e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 6.638106e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.648e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.340403e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 8.259500e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.529e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.226871e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.002669e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.107e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.095892e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.398532e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.414e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.152628e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.667650e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.237e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.548458e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.883524e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.395e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.326271e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.872458e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.960e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.662466e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.534338e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 9.229e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.888112e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.311939e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.926e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.223444e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.073235e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.416e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.948379e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.308647e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.163e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.499766e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.520309e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.361e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.230900e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.220046e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.563e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.133289e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.306086e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.760e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.329745e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.826868e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.428e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.486253e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 4.332530e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.915e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.713631e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.442698e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.316e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.805506e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.739871e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.814e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.990163e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 6.927375e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.481e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.469864e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 7.778065e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.149e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.233423e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.121182e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.467e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.969894e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.154405e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.908e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.937485e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.972551e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.995e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.304617e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.823274e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.437e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.921891e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.444183e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.682e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.398995e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 8.672938e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.199e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.494678e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.857729e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.381e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.182646e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.975094e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.636e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.386964e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.446228e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.830e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.224547e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.144036e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.104e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.480109e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.794419e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.156e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.680771e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.596059e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.336e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.655494e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.785005e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.883e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.017977e-04\n",
+      "INFO   1 (restart 0) KSP residual norm 3.372312e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.313e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.309686e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.167924e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.057e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.061262e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 3.177586e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.994e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.018029e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 6.964612e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.451e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.189851e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 6.279523e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.868e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.452416e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 7.511447e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.063e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.720013e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 8.856611e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.256e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.399368e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.112883e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.274e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.978616e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.359692e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.418e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.161890e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 7.361101e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.405e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.173884e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.996618e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.108e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.132939e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.565132e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.049e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.659845e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.695224e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.047e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.905503e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.187079e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.600e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.656329e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.269579e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.544e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.638449e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.712618e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.491e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.803324e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.873269e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.925e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.723752e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.007329e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.391e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.729302e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.463978e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.096e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.003658e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.045283e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.217e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.082928e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 3.564085e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.291e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.857006e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 7.201914e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.878e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.538102e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 4.845753e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.150e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.118517e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 3.296222e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.947e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.189706e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.399186e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.699e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.470240e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 5.567988e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.787e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.399601e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 7.204799e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.002e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.577909e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 5.360768e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.397e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.005508e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.232094e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.203e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.858728e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.665024e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.427e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.791617e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.603738e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.496e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.199480e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.054187e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.420e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.144657e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.199080e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.025e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.687933e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.077364e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.728e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.658105e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.867395e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.105e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.468188e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.014975e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.810e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.965825e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 1.024626e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.455e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.915838e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.735195e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.081e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.584345e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.478548e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.629e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.421028e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 5.179928e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.645e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.048208e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.020830e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.753e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.206651e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.935873e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.037e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.011419e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.051139e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.020e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.736813e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.532101e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.414e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.406874e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 4.936983e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.509e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.134906e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 4.083878e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.598e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.016288e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.750595e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.674e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.777277e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.131024e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.461e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.988273e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.759144e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.531e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.016621e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.293475e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.603e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.845470e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.330118e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.263e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.476548e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.110090e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.520e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.328576e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.554658e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.671e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.382142e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.639438e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.847e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.809933e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 5.595548e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.092e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.580980e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.191189e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.549e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.032769e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.430489e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.026e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.051247e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 3.880480e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.691e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.772243e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.782726e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.736e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.485357e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.164383e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.210e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.094541e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.801174e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.599e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.976577e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.037319e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.845e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.045518e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 4.606492e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.406e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.452469e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.110902e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.680e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.647077e-07\n",
+      "INFO   1 (restart 0) KSP residual norm 4.591128e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.759e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.226919e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.398689e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.675e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.374954e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.739031e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.116e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.074996e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.113700e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.019e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.719688e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.122167e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.234e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.074774e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.683517e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.475e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.401725e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.236504e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.635e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.197095e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.486352e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.649e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.303718e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 4.377064e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.357e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.435027e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.204919e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.627e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.754511e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.300933e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.407e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.160509e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.717455e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.795e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.386600e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.625646e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.800e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.273591e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.235968e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.830e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.026683e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.686670e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.322e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.604619e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.757905e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.749e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.433317e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.514430e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.728e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.872050e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.404726e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.325e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 9.838134e-07\n",
+      "INFO   1 (restart 0) KSP residual norm 4.476737e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.550e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.320943e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.963786e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.545e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.650436e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.101427e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.757e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.335113e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.944023e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.325e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.755766e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.432203e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.385e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.645920e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.999923e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.485e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.807792e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.880267e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.938e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.916292e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.343568e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.036e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.101287e-05\n",
+      "INFO   1 (restart 0) KSP residual norm 3.869266e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.513e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.305774e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.428761e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.392e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.679385e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.634349e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.638e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.283880e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.481183e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.588e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.220507e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.325827e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.880e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.769859e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.760834e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 9.976e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.765399e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.932408e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.227e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.706283e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.931455e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.453e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.872267e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.530148e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.047e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 6.679171e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.579522e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.856e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.079304e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.886641e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 9.160e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.295811e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.691529e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.092e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.878963e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.603900e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.599e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.485632e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.508565e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.814e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.542633e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.137893e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.021e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.904509e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.077158e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.300e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.128390e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.500616e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.332e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.861013e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.347643e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.869e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 8.810134e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.723497e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.226e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.202748e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 6.882681e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.722e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.861614e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.003723e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.235e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.034795e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.393840e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.833e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.839614e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.955040e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.644e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.859246e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.483807e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.939e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.071356e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.228958e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.456e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.936458e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.042544e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.670e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.023367e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.106745e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.203e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.561877e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.653129e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.376e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.043851e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.148797e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.059e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.733205e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.045828e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.801e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.355728e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 8.881381e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.770e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.560150e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.346083e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.651e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.767233e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.542568e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.448e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.007775e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 8.667861e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.163e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.821606e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 8.830855e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.311e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.744188e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.058004e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.572e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 7.090466e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.448679e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.864e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.143068e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.437320e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.257e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.354990e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.863486e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.871e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.317972e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 6.701263e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.020e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.480743e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.178862e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.602e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.112610e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.454836e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.395e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.923056e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.443416e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.911e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.640258e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.051536e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.411e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.752185e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.440414e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.031e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.506450e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.008036e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.237e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.180349e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.628470e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.074e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.544361e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.319639e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.723e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.838858e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.983750e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.429e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.312529e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.720132e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.203e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.546029e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 8.183610e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.214e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.522056e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 6.995871e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.986e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.259375e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 6.991220e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.145e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.029929e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.396598e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.781e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 5.675515e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.753694e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.852e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.110689e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.368385e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.232e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.684860e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.093418e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.111e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.305363e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 6.052632e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.625e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.000802e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 6.557221e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.639e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.610401e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 6.814104e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.610e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.225405e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.050635e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.067e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.809516e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.122075e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.041e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.947099e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.330499e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.371e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.313795e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.821071e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.277e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.322278e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.625570e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.742e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.665028e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.250307e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.411e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.679796e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 8.881366e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.287e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.822267e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.074688e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.980e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.759860e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.283909e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.639e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.560438e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 6.360251e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.786e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.845465e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 6.127923e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.154e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.512711e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.757644e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.893e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.509564e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.354537e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.221e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.062676e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.277185e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.202e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.125887e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.489925e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.436e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.634954e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.333964e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.024e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.135356e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.618772e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.359e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.969136e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 6.101086e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.055e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.286562e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.394006e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.234e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.732559e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.416480e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.281e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.889267e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.143455e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.940e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 4.336218e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.418088e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.711e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.406834e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.244527e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.306e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.736736e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.068490e-17\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.859e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.469420e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.265517e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.944e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.810799e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.074302e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.907e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.963297e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 6.694165e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.259e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.640103e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.630717e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.547e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.055751e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.898128e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.603e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.431696e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.668032e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.508e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.748707e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.863348e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.971e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.024845e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.740416e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 9.504e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.743887e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.927380e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.431e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.720082e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.914258e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.439e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.792720e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.194164e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.106e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.669681e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.657217e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.744e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.833586e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.840591e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.640e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.557283e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.347120e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.434e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.356910e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 8.308404e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.475e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.991405e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.780343e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.198e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.327664e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.292023e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.726e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.400772e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.436941e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.187e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.425145e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.953134e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.476e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.758714e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.429499e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.519e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.718264e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.186359e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.540e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.361724e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.897715e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.159e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.917224e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.977493e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.021e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.371574e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.284935e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 9.635e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.146180e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.196583e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.803e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.047510e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 6.386304e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.097e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.524872e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.430320e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 9.626e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.665204e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.517485e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 9.446e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.396043e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.702256e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.957e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.417276e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.138268e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.298e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.697724e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.769914e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.632e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.594037e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.546717e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.225e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.259565e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.553517e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.704e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.610387e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.672241e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.402e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.301534e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.602627e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.231e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.257065e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.078728e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.559e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.455347e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.138100e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 2.156e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.711816e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.762880e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.614e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.437124e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.671167e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.096e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.988400e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.413562e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.076e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.749989e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.182972e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.938e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.393374e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.757932e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.345e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.787514e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.280312e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.593e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.155247e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 5.936949e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.139e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.369579e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.836648e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.751e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.452153e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.702468e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.943e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.919118e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.055290e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.041e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.142939e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.179537e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.017e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.640092e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.177778e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.328e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.655909e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.929404e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.769e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.144692e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 4.244096e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.350e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.201065e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.858156e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.805e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.271692e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.232033e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 9.688e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.104289e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.790348e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.221e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.523125e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.397729e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.574e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.628523e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.927012e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.183e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.150345e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.959489e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 9.112e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.537808e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.741010e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.860e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.579591e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.756168e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.808e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.489739e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.708406e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.862e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.634713e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.083973e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.114e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.314955e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 6.830235e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.194e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.300231e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.779173e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.735e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.291046e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.591672e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.947e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.466491e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.703791e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.908e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.915358e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.581572e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.257e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.555365e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.710740e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.100e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.791391e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.521149e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.407e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.096781e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.186260e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.029e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.819706e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.550313e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.498e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.265219e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.083757e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.566e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.951891e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 3.089919e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.047e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.616717e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.089371e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.292e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.573005e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.844442e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.173e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.967850e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.574109e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.999e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.172270e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.360010e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.261e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.426065e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.835107e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.564e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.594308e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.627491e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.273e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.525445e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.221714e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.838e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.496212e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 8.234780e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.504e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.209112e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.888485e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.549e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.171035e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.508345e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.948e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.092003e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.270584e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.074e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.744804e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.398043e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.013e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.479764e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.590548e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.075e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.056487e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.246052e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.092e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.000360e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.641631e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.804e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.459955e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.380565e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.612e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.276959e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.008948e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.901e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.742682e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.594431e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 9.459e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.777157e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.843025e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.037e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.646674e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.614105e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 9.802e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.882145e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.284058e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.822e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.982313e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.307199e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.594e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.262533e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.610790e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.119e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.663277e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.427291e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.359e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.347959e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.114413e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.746e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.668212e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.954123e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.967e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.047796e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.629390e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.957e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.086970e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.502690e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.200e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.876427e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.180119e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.289e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.605442e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.368160e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.522e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.541934e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.630730e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.058e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.413716e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.014346e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.345e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.772013e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.311137e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.337e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.223514e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.399102e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.292e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.289370e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.042963e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.089e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.461036e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.277214e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 9.253e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.025500e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.749631e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.638e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.897806e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.380893e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.276e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.899996e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.104308e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.812e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.952407e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.311785e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.719e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.065016e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.501134e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.269e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.660204e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.436932e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.402e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.103091e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.050726e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.996e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.776708e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.495498e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.344e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.865821e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.362292e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.301e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.010443e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.579804e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.858e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.808742e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.135812e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.280e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.588943e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.170863e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.369e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.878911e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.452873e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.733e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.688161e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.009721e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.476e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.441700e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.053480e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.410e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.145965e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.341171e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.250e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.305576e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.044901e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.003e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.159747e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.102686e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 9.736e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.319028e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.746865e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.533e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.256940e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.236546e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.479e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.052450e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.202566e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.859e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.990961e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.506250e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.565e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.849473e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.485805e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.034e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.532763e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.236999e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.884e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.888657e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.023133e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.417e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.804319e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.383714e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.201e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.703664e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.232470e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.234e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.955064e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.400040e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.161e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.857339e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.253014e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.746e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.788773e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.218240e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.810e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.359827e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.455791e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.169e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.670705e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.936787e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.252e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.208249e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.855239e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.401e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.098346e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.326338e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.321e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.399270e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.156362e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.264e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.961887e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.118682e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 1.080e-12)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.568014e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.694811e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.600e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.573381e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.234043e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.795e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.228394e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.243496e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.580e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.025806e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.450621e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.161e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.716049e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.394742e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.128e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.455191e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.221727e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.976e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.835175e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 8.452032e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.606e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.867009e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.007129e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.394e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.617526e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.188727e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.349e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.950180e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.284525e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.587e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.949949e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.299288e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.663e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.080298e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.162054e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.586e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.740693e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.404454e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.124e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.535636e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.927079e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.600e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.220764e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.741177e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.840e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.991015e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.218176e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.118e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.559456e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.283349e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.229e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.846665e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.613563e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.738e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.736968e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.622352e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.928e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.778870e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.092482e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.931e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.358564e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.391465e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.900e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.014477e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.385235e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.876e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.725678e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.468829e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.512e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.457654e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.193647e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.857e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.832578e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.468519e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.075e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.969571e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.081604e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.492e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.604320e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.073355e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.690e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.967443e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.529227e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.773e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.029465e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.357399e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.688e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.350041e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.190626e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.066e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.971454e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.236726e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.162e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.491920e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.974572e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.924e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.306699e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.712610e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.425e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.872607e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.089608e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.819e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.722553e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.349823e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.836e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.761312e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.600473e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 9.087e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.848182e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.827822e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.418e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.898674e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.227041e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.233e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.443878e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.407566e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.760e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.981118e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.345849e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.793e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.839836e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.288258e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.002e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.485277e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.228219e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.942e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.791915e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 8.124172e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.534e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.064973e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.131039e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.477e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.636947e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.011174e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.177e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.043450e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.493902e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.311e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.086072e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.402564e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.723e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.582855e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.186615e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.594e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.054716e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.270521e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.159e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.552927e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.015841e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.896e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.346334e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.565818e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.673e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.790989e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.754043e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.446e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.817501e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.338531e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.365e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.711861e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.506681e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.801e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.891645e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.533370e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.303e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.915654e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.148444e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.939e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.420476e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.369164e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.657e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.004590e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.451186e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.239e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.008794e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.117644e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.564e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.457281e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.361606e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.541e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.696123e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 7.813048e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.606e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.109948e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.257809e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.961e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.692850e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.013164e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.985e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.210349e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.323293e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.987e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.094426e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.372899e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.555e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.749695e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.193780e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.341e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 3.042706e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.237713e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.068e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.675867e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 2.018800e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.544e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.276177e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.715565e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.537e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.769583e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.046056e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.112e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.827043e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.305902e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.148e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.730609e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.518367e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.774e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.852866e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.579104e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.535e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.909201e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.156443e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 3.975e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.341896e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.418521e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.057e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.210232e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.483963e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.714e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.143285e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 9.814006e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.579e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.393798e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.414098e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.907e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.611691e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 8.619395e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.348e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.131704e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.328790e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.233e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.758434e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.032997e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.875e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.448612e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.075347e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.392e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.161559e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.361483e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.299e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.809443e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.198434e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.266e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.887421e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.170194e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.053e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.742809e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.966943e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.171e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.050504e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.568670e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.650e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.705951e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 8.847378e-19\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.186e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.715034e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.297164e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 7.563e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 1.829531e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.624061e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 8.877e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.694810e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.427401e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 5.297e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.794455e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.125826e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.029e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.199026e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.439806e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.547e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.488954e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.187754e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.772e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.221951e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.010008e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 4.546e-13)\n",
+      "INFO   Residual norms for GMRES solve\n",
+      "INFO   0 (restart 0) KSP residual norm 2.286311e-06\n",
+      "INFO   1 (restart 0) KSP residual norm 1.587318e-18\n",
+      "INFO GMRES solver converged in 1 iteration (avg. reduction factor: 6.943e-13)\n",
+      "INFO  Found 4 converged eigenvalues (sigma = -1.297310e+06)\n",
+      "INFO  eig 0: kn = 1.123307e+03+2.571722e-11i, n_eff = 2.465565e+00+5.644716e-14i\n",
+      "INFO  eig 1: kn = 9.582608e+02+4.270859e-08i, n_eff = 2.103303e+00+9.374179e-11i\n",
+      "INFO  eig 2: kn = 9.582575e+02+3.458361e-09i, n_eff = 2.103296e+00+7.590814e-12i\n",
+      "INFO  eig 3: kn = 9.582228e+02-1.450928e-09i, n_eff = 2.103219e+00-3.184666e-12i\n",
+      "INFO Computing solution error estimates and performing postprocessing\n",
+      "INFO      m,       Re{kn} (1/m),       Im{kn} (1/m),          Re{n_eff},          Im{n_eff},      Error (Bkwd.),       Error (Abs.)\n",
+      "INFO      1,      +9.993833e+06,      +2.288009e-07,      +2.465565e+00,      +5.644716e-14,      +6.699217e-16,      +8.139743e-13\n",
+      "INFO  Wrote mode 1 to disk (Paraview)\n",
+      "INFO      2,      +8.525452e+06,      +3.799696e-04,      +2.103303e+00,      +9.374179e-11,      +6.895569e-15,      +7.979476e-13\n",
+      "INFO  Wrote mode 2 to disk (Paraview)\n",
+      "INFO      3,      +8.525423e+06,      +3.076833e-05,      +2.103296e+00,      +7.590814e-12,      +2.036645e-15,      +2.356745e-13\n",
+      "INFO      4,      +8.525114e+06,      -1.290861e-05,      +2.103219e+00,      -3.184666e-12,      +1.709535e-15,      +1.977882e-13\n",
+      "INFO Completed 0 iterations of adaptive mesh refinement (AMR):\n",
+      "INFO  Indicator norm = 4.035e-02, global unknowns = 167329\n",
+      "INFO  Max. iterations = 0, tol. = 1.000e-02\n",
+      "INFO Estimated peak per-rank memory usage is: Min. 1.0G, Max. 1.0G, Avg. 1.0G, Total 1.0G\n",
+      "INFO Estimated peak per-node memory usage is: Min. 1.0G, Max. 1.0G, Avg. 1.0G, Total 1.0G\n",
+      "INFO Elapsed Time Report (s)           Min.        Max.        Avg.\n",
+      "INFO ==============================================================\n",
+      "INFO Initialization                   0.040       0.040       0.040\n",
+      "INFO   Mesh Preprocessing             0.101       0.101       0.101\n",
+      "INFO Operator Construction            0.361       0.361       0.361\n",
+      "INFO   Preconditioner               105.506     105.506     105.506\n",
+      "INFO Eigenvalue Solve                73.111      73.111      73.111\n",
+      "INFO Estimation                       0.066       0.066       0.066\n",
+      "INFO   Construction                   8.715       8.715       8.715\n",
+      "INFO   Solve                          1.487       1.487       1.487\n",
+      "INFO Postprocessing                   8.851       8.851       8.851\n",
+      "INFO   Paraview                       3.190       3.190       3.190\n",
+      "INFO Disk IO                          0.088       0.088       0.088\n",
+      "INFO --------------------------------------------------------------\n",
+      "INFO Total                          201.746     201.746     201.746\n",
+      "INFO Peak Memory                   Per-Node       Total   Total HWM\n",
+      "INFO ==============================================================\n",
+      "INFO Initialization                    4.2M        4.2M        4.2M\n",
+      "INFO   Mesh Preprocessing             10.2M       10.2M       14.4M\n",
+      "INFO Operator Construction           193.3M      193.3M      207.7M\n",
+      "INFO   Preconditioner                584.1M      584.1M      791.8M\n",
+      "INFO Eigenvalue Solve                176.1M      176.1M      967.8M\n",
+      "INFO Estimation                        0.0K        0.0K      967.8M\n",
+      "INFO   Construction                   17.1M       17.1M      984.9M\n",
+      "INFO   Solve                           0.0K        0.0K      984.9M\n",
+      "INFO Postprocessing                    0.0K        0.0K      984.9M\n",
+      "INFO   Paraview                        0.0K        0.0K      984.9M\n",
+      "INFO Disk IO                           7.2M        7.2M      992.2M\n",
+      "INFO --------------------------------------------------------------\n",
+      "INFO Total                          1002.5M     1002.5M     1002.5M\n",
+      "INFO Simulation completed successfully\n",
+      "INFO Results saved to palace-sim-mzm-pn-opt/output/palace\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "mode 1: k_n = +9.993833e+06+2.288009e-07j, n_eff = +2.465565e+00+5.644716e-14j, eta_eff ~= 152.80-0.00j\n",
+      "mode 2: k_n = +8.525452e+06+3.799696e-04j, n_eff = +2.103303e+00+9.374179e-11j, eta_eff ~= 179.11-0.00j\n",
+      "mode 3: k_n = +8.525423e+06+3.076833e-05j, n_eff = +2.103296e+00+7.590814e-12j, eta_eff ~= 179.11-0.00j\n",
+      "mode 4: k_n = +8.525114e+06-1.290861e-05j, n_eff = +2.103219e+00-3.184666e-12j, eta_eff ~= 179.12+0.00j\n"
+     ]
+    }
+   ],
+   "source": [
+    "opt_results = sim_optical.run_local(verbose=True)\n",
+    "opt_results.print()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8c06ca56",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# --- Optical mode in the rib waveguide (1550 nm) ---\n",
+    "from gsim.palace import plot_fields_2d\n",
+    "\n",
+    "pl = plot_fields_2d(\n",
+    "    OPT_OUTPUT_DIR,\n",
+    "    field=OPT_FIELD,\n",
+    "    title=OPT_FIELD_TITLE,\n",
+    "    interactive=True,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "14e28ef2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# --- Rib waveguide zoom: optical physical groups (all Si) ---\n",
+    "pl = plot_fields_2d(\n",
+    "    OPT_OUTPUT_DIR,\n",
+    "    field=OPT_FIELD,\n",
+    "    physical_groups=OPT_RIB_PHYSICAL_GROUPS,\n",
+    "    title=\"Optical Mode |E| in the Rib Waveguide (1550 nm, zoomed)\",\n",
+    "    interactive=True,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "23",
+   "metadata": {},
+   "source": [
+    "## Summary\n",
+    "\n",
+    "The geometry has been built and meshed for both RF (50 GHz) and optical (193 THz / 1550 nm) analysis.\n",
+    "\n",
+    "**Cross-section elements:**\n",
+    "| Component | Layer | y-range (um) | z-range (um) | Material | sigma (S/m) |\n",
+    "|---|---|---|---|---|---|\n",
+    "| Rib core | WG (1,0) | [-20.2, -19.8] | [0, 0.22] | Si (intrinsic) | 2 |\n",
+    "| Slab (90 nm) | SLAB90 (3,0) | [-40.2, +0.2] | [0, 0.09] | Si (intrinsic) | 2 |\n",
+    "| PN junction (P) | P (21,0) | [-20.0, -19.8] | [0, 0.22] | doped Si (p_rib) | 1.6x10^3 |\n",
+    "| PN junction (N) | N (20,0) | [-20.2, -20.0] | [0, 0.22] | doped Si (n_rib) | 1.6x10^3 |\n",
+    "| P+ graded inner | PP (23,0) | [-18.3, -16.3] | [0, 0.09] | doped Si (pp_slab_0) | 2x10^4 |\n",
+    "| P+ graded outer | PP (23,1) | [-15.3, -13.3] | [0, 0.09] | doped Si (pp_slab_1) | 8x10^4 |\n",
+    "| N+ graded inner | NPP (24,0) | [-21.7, -23.7] | [0, 0.09] | doped Si (npp_slab_0) | 2x10^4 |\n",
+    "| N+ graded outer | NPP (24,1) | [-24.7, -26.7] | [0, 0.09] | doped Si (npp_slab_1) | 8x10^4 |\n",
+    "| Vias (S to P+) | VIAC/VIA1/VIA2 | [-15.0, -9.0] | [0.09, 3.2] | W/Al | 3.5x10^7 |\n",
+    "| Vias (G to N+) | VIAC/VIA1/VIA2 | [-31.0, -25.0] | [0.09, 3.2] | W/Al | 3.5x10^7 |\n",
+    "| CPW signal | M1 (41,0) | [-10, +10] | [3.2, 4.2] | Al (1 um) | 3.5x10^7 |\n",
+    "| CPW ground (top) | M1 (41,0) | [+30, +70] | [3.2, 4.2] | Al (1 um) | 3.5x10^7 |\n",
+    "| CPW ground (bot) | M1 (41,0) | [-70, -30] | [3.2, 4.2] | Al (1 um) | 3.5x10^7 |\n",
+    "\n",
+    "**Material modelling notes:**\n",
+    "- Doping regions are modelled as **semiconductors** (finite sigma from the Drude free-carrier model), not metals. This avoids short-circuiting the PN junction.\n",
+    "- Conductivities are derived from $\\sigma = q\\mu N$ with typical dopant concentrations ($N \\sim 10^{19}\\ \\text{cm}^{-3}$ for the junction, $\\sim 10^{20}\\ \\text{cm}^{-3}$ for the contacts).\n",
+    "- Doping on each side of the rib uses a **configurable piecewise gradient** via `make_doping_profile()`, and the whole cross-section assembly is wrapped by `build_doped_cross_section()`.\n",
+    "- The **depletion region** and voltage-dependent capacitance are NOT modelled here — this is a linear small-signal analysis at a fixed bias point.\n",
+    "- The **plasma-dispersion effect** is not applied to the optical simulation; the rib is treated as intrinsic Si at 1550 nm.\n",
+    "\n",
+    "**Optical-only component:**\n",
+    "- The optical run (`sim_optical`) uses a **simplified component** — the same\n",
+    "  rib + slab + PN junction (\"doping profile\") polygons, but no electrodes,\n",
+    "  vias, or graded doping.\n",
+    "- Every device region maps to **plain silicon** in `build_optical_cross_section()`,\n",
+    "  so the optical mode sees one homogeneous Si body in a **uniform SiO2 cladding**.\n",
+    "- The background medium is SiO2, not air: `set_airbox(material=\"sio2\", ...)`\n",
+    "  fills the padded 2D domain with the cladding material (default is air).\n",
+    "- Material dispersion is evaluated at `F_OPT` by the boundary-mode config\n",
+    "  generator: Si -> eps~12.09 (n~3.478), SiO2 -> eps~2.09 (n~1.444) at 1550 nm.\n",
+    "\n",
+    "**Next steps (user action):**\n",
+    "1. Verify the zoomed cross-section plot shows the rib (centred at y=-20), PN junction, graded doping, and vias.\n",
+    "2. Run `sim.run_local(verbose=True)` with a Palace CPU runner installed (`pip install gsim[palace-toolkit-cpu]`). 2D\n",
+    "   mode analysis defaults to a single MPI rank + OpenMP threads; pass `num_processes=1` explicitly if you want\n",
+    "   to be explicit about it.\n",
+    "3. Run `sim_optical.run_local(verbose=True)` for the optical mode.\n",
+    "4. Use `gsim.palace.plot_fields_2d()` to visualise mode profiles, and `gsim.palace.plot_plane_section()` for cross-section physical groups.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "24",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "=== RF cross-section regions (x=0) ===\n",
+      "  core          mat=si          y=[-20.20,-19.80]  z=[0.000,0.220]\n",
+      "  slab90        mat=si          y=[-50.20, 50.20]  z=[0.000,0.090]\n",
+      "  via_contact   mat=Aluminum    y=[-29.35,-28.65]  z=[0.090,1.100]\n",
+      "  via_contact   mat=Aluminum    y=[ -9.35, -8.65]  z=[0.090,1.100]\n",
+      "  metal1        mat=Aluminum    y=[-70.00,-27.65]  z=[1.100,2.100]\n",
+      "  metal1        mat=Aluminum    y=[-10.35, 10.00]  z=[1.100,2.100]\n",
+      "  metal1        mat=Aluminum    y=[ 30.00, 70.00]  z=[1.100,2.100]\n",
+      "  pp_slab_0     mat=pp_slab_0   y=[-19.80,-17.80]  z=[0.000,0.090]\n",
+      "  pp_slab_1     mat=pp_slab_1   y=[-17.80,-15.80]  z=[0.000,0.090]\n",
+      "  npp_slab_0    mat=npp_slab_0  y=[-22.20,-20.20]  z=[0.000,0.090]\n",
+      "  npp_slab_1    mat=npp_slab_1  y=[-24.20,-22.20]  z=[0.000,0.090]\n",
+      "  p_rib         mat=p_rib       y=[-20.00,-19.80]  z=[0.000,0.220]\n",
+      "  n_rib         mat=n_rib       y=[-20.20,-20.00]  z=[0.000,0.220]\n",
+      "\n",
+      "=== Optical cross-section regions (x=0) ===\n",
+      "  core          mat=si          y=[-20.20,-19.80]  z=[0.000,0.220]\n",
+      "  slab          mat=si          y=[-50.20, 50.20]  z=[0.000,0.090]\n",
+      "  p_rib         mat=si          y=[-20.00,-19.80]  z=[0.000,0.220]\n",
+      "  n_rib         mat=si          y=[-20.20,-20.00]  z=[0.000,0.220]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Quick verification: dump the 2D cross-section layer regions\n",
+    "print(\"=== RF cross-section regions (x=0) ===\")\n",
+    "for r in section:\n",
+    "    print(\n",
+    "        f\"  {r.layer_name:12s}  mat={r.material:10s}  \"\n",
+    "        f\"y=[{r.y0:6.2f},{r.y1:6.2f}]  z=[{r.zmin:5.3f},{r.zmax:5.3f}]\"\n",
+    "    )\n",
+    "print(\"\\n=== Optical cross-section regions (x=0) ===\")\n",
+    "for r in section_opt:\n",
+    "    print(\n",
+    "        f\"  {r.layer_name:12s}  mat={r.material:10s}  \"\n",
+    "        f\"y=[{r.y0:6.2f},{r.y1:6.2f}]  z=[{r.zmin:5.3f},{r.zmax:5.3f}]\"\n",
+    "    )"
+   ]
+  }
+ ],
+ "metadata": {
+  "jupytext": {
+   "formats": "ipynb,py:percent"
+  },
+  "kernelspec": {
+   "display_name": ".venv (3.12.3.final.0)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/nbs/palace_2d_twmzm.py b/nbs/palace_2d_twmzm.py
new file mode 100644
index 00000000..9b955814
--- /dev/null
+++ b/nbs/palace_2d_twmzm.py
@@ -0,0 +1,679 @@
+# ---
+# jupyter:
+#   jupytext:
+#     formats: ipynb,py:percent
+#     text_representation:
+#       extension: .py
+#       format_name: percent
+#       format_version: '1.3'
+#       jupytext_version: 1.19.2
+#   kernelspec:
+#     display_name: .venv (3.12.3.final.0)
+#     language: python
+#     name: python3
+# ---
+
+# %% [markdown]
+# # Palace 2D Mode Analysis: Travelling-Wave Mach-Zehnder Modulator
+#
+# This notebook builds a simplified cross-section of a Travelling-Wave Mach-Zehnder Modulator (TW-MZM) with a PN-junction embedded in a rib waveguide, using CPW electrodes for RF modulation.
+#
+# **Cross-section geometry (from literature):**
+# - **SOI substrate**: 220 nm Si on 2 um buried oxide (BOX)
+# - **Rib waveguide**: 400 nm width, 90 nm slab height
+# - **CPW electrodes**: Aluminium, 1 um thick, signal width $w=20$ um, gap $g=20$ um
+# - **PN junction**: Centred in the rib with P+/N+ contact regions in the slab
+#
+# We use `BoundaryModeSim` (Palace 2D eigenmode solver) to compute both RF and optical modes.
+#
+# **Requirements:**
+# - gdsfactory + generic PDK (`gf.gpdk`)
+# - A Palace binary resolved internally by `run_local()` (e.g. `palace-toolkit-cpu`, `PALACE_BIN`, or `palace` on PATH)
+# - [GDSFactory+](https://gdsfactory.com) account only for cloud runs
+#
+# **Workflow:** parameters are grouped next to the stage they configure — geometry &amp; materials, then RF, then optical.
+#
+
+# %% [markdown]
+# ## Geometry &amp; materials parameters
+#
+# Define the layout dimensions, the substrate/metal stack, and the doping
+# (geometry + material) for the rib and graded slab regions. These are consumed
+# by the geometry build and by
+# `gsim.common.cross_section.build_doped_cross_section()`.
+#
+# The generic helpers used here are PDK-agnostic — no hardcoded values live in
+# the notebook.
+#
+# **Layer assignments (gpdk):**
+# - `WG` (1,0): Waveguide core (220 nm Si, 400 nm wide)
+# - `SLAB90` (3,0): 90 nm slab regions
+# - `N` (20,0) / `P` (21,0): PN junction doping
+# - `NPP` (24,0) / `PP` (23,0): N+/P+ graded contact doping (via `make_doping_profile`)
+# - `M1` (41,0): CPW electrodes (Al, 1 um thick)
+#
+
+# %%
+# =============================================================================
+#  Geometry & materials parameters
+# =============================================================================
+
+# --- Device / rib geometry (um) ---------------------------------------------
+RIB_WIDTH = 0.4  # rib waveguide width
+RIB_HEIGHT = 0.22  # rib waveguide height (z)
+SLAB_THICKNESS = 0.09  # slab height (z) on each side of the rib
+SLAB_HALF = 50.0  # slab half-width (y, on each side of the rib)
+SIG_WIDTH = 20.0  # CPW signal electrode width
+GAP_WIDTH = 20.0  # CPW signal-to-ground gap
+GND_WIDTH = 40.0  # CPW ground electrode width
+LENGTH = 10.0  # layout length along the propagation axis (x)
+TOTAL_HALF = SIG_WIDTH / 2 + GAP_WIDTH + GND_WIDTH  # lateral half-extent
+RIB_CENTER_Y = -(SIG_WIDTH / 2 + GAP_WIDTH / 2)  # rib centre y (=-20)
+
+VIA_SIZE = 2.7  # via_stack footprint (square)
+VIA_S_TO_P_Y = -9.0  # via from signal to P+ contact (y)
+VIA_G_TO_N_Y = -29.0  # via from ground to N+ contact (y)
+
+# --- Substrate stack (um) -----------------------------------------------------
+BOX_THICKNESS = 2.0  # buried-oxide thickness (below z=0)
+METAL1_ZMIN = 1.1  # metal1 bottom (top of the oxide stack)
+METAL1_THICKNESS = 1.0  # CPW electrode thickness on metal1
+
+# --- PN junction / doping material model -------------------------------------
+SI_PERMITTIVITY = 11.9
+FMAX_RF_MATERIAL = 200e9  # validity range of the constant-eps doping models (Hz)
+RIB_DOPING_SIGMA = 1.6e3  # p_rib / n_rib junction conductivity (S/m)
+
+# Graded slab doping {side: [(width_um, sigma_S_per_m), ...]}, from the rib edge.
+DOPING_PROFILE = {
+    "upper": [(2.0, 2.0e4), (2.0, 8.0e4)],  # P+ graded (toward signal)
+    "lower": [(2.0, 2.0e4), (2.0, 8.0e4)],  # N+ graded (toward ground)
+}
+DOPING_SIDES = {  # config passed to make_doping_profile()
+    "upper": {"base_layer": (23, 0), "name_prefix": "pp_slab_", "sign": 1},
+    "lower": {"base_layer": (24, 0), "name_prefix": "npp_slab_", "sign": -1},
+}
+
+# --- Cross-section plane ------------------------------------------------------
+CROSS_SECTION_AXIS = "x"
+CROSS_SECTION_VALUE = 0.0
+
+# %% [markdown]
+# ## Build TW-MZM cross-section geometry
+#
+# The 3D layout component is sliced at $x=0$ for 2D mode analysis. The graded
+# doping regions are created with `make_doping_profile()` (no hardcoded geometry).
+#
+
+# %%
+import gdsfactory as gf
+
+from gsim.common.cross_section import build_optical_cross_section
+from gsim.common.stack.doping import make_doping_profile
+
+gf.gpdk.PDK.activate()
+
+LAYER = gf.gpdk.LAYER
+
+
+def centered_rect(wx: float, wy: float, layer) -> gf.Component:
+    r = gf.Component()
+    r << gf.c.rectangle((wx, wy), centered=True, layer=layer)
+    return r
+
+
+def _add_device_core(comp: gf.Component) -> None:
+    """Rib + slab + PN junction — shared by the RF and optical components.
+
+    The P/N rectangles are the same "doping profile" polygons in both, so the
+    optical cross-section still shows the junction shape. The optical stack
+    maps all four regions to plain silicon.
+    """
+    # 1. Rib waveguide core (PN junction sits inside it)
+    wg = comp << centered_rect(LENGTH, RIB_WIDTH, LAYER.WG)
+    wg.y = RIB_CENTER_Y
+
+    # 2. Slab (90 nm)
+    slab = comp << centered_rect(LENGTH, 2 * SLAB_HALF + RIB_WIDTH, LAYER.SLAB90)
+    slab.y = 0.0
+
+    # 3. PN junction (P above / N below the rib centre)
+    p_half = comp << gf.c.rectangle((LENGTH, RIB_WIDTH / 2), layer=LAYER.P)
+    p_half.y = RIB_CENTER_Y + RIB_WIDTH / 4
+    n_half = comp << gf.c.rectangle((LENGTH, RIB_WIDTH / 2), layer=LAYER.N)
+    n_half.y = RIB_CENTER_Y - RIB_WIDTH / 4
+
+
+def _build_rf_component() -> tuple[gf.Component, dict]:
+    """Full TW-MZM cross-section: device core + graded doping + CPW + vias."""
+    comp = gf.Component()
+    _add_device_core(comp)
+
+    # 4. Graded N+/P+ slab doping (contiguous, no gaps)
+    doping_result = make_doping_profile(
+        comp,
+        length=LENGTH,
+        rib_center_y=RIB_CENTER_Y,
+        rib_width=RIB_WIDTH,
+        profile=DOPING_PROFILE,
+        sides=DOPING_SIDES,
+        zmin=0.0,
+        zmax=SLAB_THICKNESS,
+        permittivity=SI_PERMITTIVITY,
+        fmax=FMAX_RF_MATERIAL,
+    )
+
+    # 5. CPW electrodes (M1)
+    comp << centered_rect(LENGTH, SIG_WIDTH, LAYER.M1)
+    gnd_top = comp << centered_rect(LENGTH, GND_WIDTH, LAYER.M1)
+    gnd_top.y = SIG_WIDTH / 2 + GAP_WIDTH + GND_WIDTH / 2
+    gnd_bot = comp << centered_rect(LENGTH, GND_WIDTH, LAYER.M1)
+    gnd_bot.y = -(SIG_WIDTH / 2 + GAP_WIDTH + GND_WIDTH / 2)
+
+    # 6. Vias at x=0 (signal-to-P+, ground-to-N+)
+    via_s_to_p = comp << gf.c.via_stack(
+        layers=("SLAB90", "M1"), vias=("viac", None), size=(VIA_SIZE, VIA_SIZE)
+    )
+    via_s_to_p.x = 0.0
+    via_s_to_p.y = VIA_S_TO_P_Y
+
+    via_g_to_n = comp << gf.c.via_stack(
+        layers=("SLAB90", "M1"), vias=("viac", None), size=(VIA_SIZE, VIA_SIZE)
+    )
+    via_g_to_n.x = 0.0
+    via_g_to_n.y = VIA_G_TO_N_Y
+
+    return comp, doping_result
+
+
+def _build_optical_component() -> gf.Component:
+    """Optical-only cross-section: rib + slab + PN junction (all silicon).
+
+    No electrodes, vias, or graded doping — the optical mode sees a single
+    homogeneous Si body embedded in the uniform SiO2 cladding stack.
+    """
+    comp = gf.Component()
+    _add_device_core(comp)
+    return comp
+
+
+# --- RF component (electrodes, vias, graded doping) ------------------------
+comp, doping_result = _build_rf_component()
+
+# --- Optical component (rib + slab + PN junction only) ---------------------
+comp_optical = _build_optical_component()
+
+# -- Plot ----------------------------------------------------------------------
+_cc = comp.copy()
+_cc.draw_ports()
+_cc.plot()
+
+# %% [markdown]
+# ## Inspect 2D cross-section
+#
+# The reusable `gsim.common.cross_section.build_doped_cross_section()` helper
+# assembles the base PDK stack, overrides `metal1`, registers the gradient doping
+# and PN-junction rib layers, and extracts the 2D cross-section at $x=0$.
+#
+
+# %%
+# Make the helper's diagnostics visible
+import logging
+
+logging.basicConfig(level=logging.INFO, format="%(levelname)s %(message)s")
+
+from gsim.common.cross_section import build_doped_cross_section
+
+stack, section = build_doped_cross_section(
+    comp,
+    axis=CROSS_SECTION_AXIS,
+    value=CROSS_SECTION_VALUE,
+    substrate_thickness=BOX_THICKNESS,
+    metal1=(METAL1_ZMIN, METAL1_THICKNESS),
+    doping=doping_result,
+    rib_layers=[
+        ("p_rib", LAYER.P, RIB_DOPING_SIGMA),
+        ("n_rib", LAYER.N, RIB_DOPING_SIGMA),
+    ],
+    rib_height=RIB_HEIGHT,
+    permittivity=SI_PERMITTIVITY,
+    fmax=FMAX_RF_MATERIAL,
+)
+
+# %% [markdown]
+# ## Optical-only cross-section
+#
+# The optical analysis uses a simplified component: the same rib + slab + PN
+# junction (identical "doping profile" polygons) but **no** electrodes, vias, or
+# graded doping. Every device region maps to plain silicon, so the optical mode
+# sees one homogeneous Si body embedded in a uniform SiO2 cladding.
+#
+# `gsim.common.cross_section.build_optical_cross_section()` assembles the
+# minimal all-dielectric `LayerStack` and extracts the 2D cross-section at $x=0$.
+
+# %%
+# Uniform SiO2 cladding height above z=0 (um)
+OPT_CLAD_TOP = 3.0
+
+stack_opt, section_opt = build_optical_cross_section(
+    comp_optical,
+    axis=CROSS_SECTION_AXIS,
+    value=CROSS_SECTION_VALUE,
+    device_layers={
+        "core": (LAYER.WG, 0.0, RIB_HEIGHT),
+        "slab": (LAYER.SLAB90, 0.0, SLAB_THICKNESS),
+        "p_rib": (LAYER.P, 0.0, RIB_HEIGHT),
+        "n_rib": (LAYER.N, 0.0, RIB_HEIGHT),
+    },
+    substrate_thickness=BOX_THICKNESS,
+    cladding_top=OPT_CLAD_TOP,
+)
+
+print("Optical stack layers:", sorted(stack_opt.layers.keys()))
+print("Optical cladding:", stack_opt.dielectrics)
+
+# %% [markdown]
+# ### Optical cross-section plot
+#
+# The PN junction still shows its P/N profile, but both regions and the slab are
+# the same silicon material.
+
+# %%
+import matplotlib.pyplot as plt
+
+from gsim.palace import plot_plane_section
+
+PLOT_ZOOM_OPT = {"h_range": (-4.0, 4.0), "v_range": (-0.6, 1.5)}
+PLOT_COLORS_OPT = {
+    "core": "#c0392b",  # rib Si
+    "slab": "#e67e22",  # slab Si
+    "p_rib": "#2980b9",  # PN junction P region (Si)
+    "n_rib": "#27ae60",  # PN junction N region (Si)
+}
+PLOT_TITLE_OPT = (
+    "Optical cross-section: rib + slab + PN junction (all Si, SiO2 cladding)"
+)
+
+plot_plane_section(
+    section_opt,
+    colors=PLOT_COLORS_OPT,
+    h_range=PLOT_ZOOM_OPT["h_range"],
+    v_range=PLOT_ZOOM_OPT["v_range"],
+    title=PLOT_TITLE_OPT,
+)
+plt.tight_layout()
+plt.show()
+
+# %% [markdown]
+# ### Optical material properties (1550 nm)
+#
+# The PDK stack materials resolve to their Sellmeier optical constants at the
+# simulation wavelength. The Palace boundary-mode config generator evaluates
+# dispersion at `F_OPT` automatically; the values below are for reference.
+
+# %%
+import math
+
+from gsim.common.stack.materials import resolve_material_at_wavelength
+
+LAMBDA_OPT = 1.55  # reference wavelength (um)
+
+si_opt = resolve_material_at_wavelength("si", LAMBDA_OPT)
+sio2_opt = resolve_material_at_wavelength("sio2", LAMBDA_OPT)
+print(
+    f"si   @ {LAMBDA_OPT:.2f} um: eps={si_opt.permittivity_scalar:.4f}  n={math.sqrt(si_opt.permittivity_scalar):.4f}"
+)
+print(
+    f"sio2 @ {LAMBDA_OPT:.2f} um: eps={sio2_opt.permittivity_scalar:.4f}  n={math.sqrt(sio2_opt.permittivity_scalar):.4f}"
+)
+
+# %% [markdown]
+# ## Plot the 2D cross-section
+#
+# The physical-group regions are rendered with the reusable
+# `gsim.palace.plot_plane_section()`. The full layout spans ~140 um, so we zoom
+# on the central region to show the rib, PN junction, graded doping and vias.
+#
+
+# %%
+# --- Cross-section plot parameters (physical-group regions) ---------------
+PLOT_ZOOM = {"h_range": (-15.0, 15.0), "v_range": (-0.5, 5.0)}
+PLOT_COLORS = {
+    "core": "#c0392b",  # rib Si -- red
+    "slab90": "#e67e22",  # slab Si -- orange
+    "p_rib": "#2980b9",  # P doping -- blue
+    "pp_slab_0": "#8e44ad",  # P+ graded inner -- purple
+    "pp_slab_1": "#a569bd",  # P+ graded outer -- light purple
+    "n_rib": "#27ae60",  # N doping -- green
+    "npp_slab_0": "#4460ad",  # N+ graded inner -- indigo
+    "npp_slab_1": "#5b7dcf",  # N+ graded outer -- light indigo
+    "metal1": "#7f8c8d",  # CPW electrodes (Al) -- grey
+    "metal2": "#7f8c8d",
+    "metal3": "#7f8c8d",
+    "via_contact": "#f1c40f",  # via -- gold
+    "via1": "#f1c40f",
+    "via2": "#f1c40f",
+}
+PLOT_TITLE = "TW-MZM cross-section (zoomed on rib + doping + signal electrode)"
+
+# %%
+import matplotlib.pyplot as plt
+
+from gsim.palace import plot_plane_section
+
+plot_plane_section(
+    section,
+    colors=PLOT_COLORS,
+    h_range=PLOT_ZOOM["h_range"],
+    v_range=PLOT_ZOOM["v_range"],
+    title=PLOT_TITLE,
+)
+plt.tight_layout()
+plt.show()
+
+# %% [markdown]
+# ## RF simulation (50 GHz)
+#
+# Configure the 50 GHz BoundaryMode run: simulation airbox, mesh, number of
+# modes, output directory, and the field quantities to plot.
+#
+
+# %%
+# =============================================================================
+#  RF parameters (50 GHz BoundaryMode run)
+# =============================================================================
+
+# --- Simulation box (airbox + mesh margins, um) -----------------------------
+AIRBOX = {"margin_x": 50.0, "margin_y": 50.0, "z_above": 100.0, "z_below": 100.0}
+MESH_MARGIN_X = 0.0
+MESH_MARGIN_Y = 50.0
+
+# --- RF solver settings -----------------------------------------------------
+F_RF = 50e9
+NUM_RF_MODES = 2
+RF_OUTPUT_DIR = "./palace-sim-mzm-pn"
+RF_MESH = {
+    "preset": "default",
+    "refined_mesh_size": 0.05,
+    "max_mesh_size": 40.0,
+    "fmax": 150e9,
+}
+
+# --- RF post-processing -----------------------------------------------------
+RF_FIELD = "E_real"
+RF_FIELD_TITLE = "RF Mode |E| at x=0 (50 GHz)"
+RIB_PHYSICAL_GROUPS = [
+    "n_rib",
+    "npp_slab_0",
+    "npp_slab_1",
+    "p_rib",
+    "pp_slab_0",
+    "pp_slab_1",
+]
+
+# --- PN junction lumped model -------------------------------------------------
+PN_JUNCTION_CAPACITANCE = 1e-15  # F, on the p_rib / n_rib interface
+
+# %%
+from gsim.palace import BoundaryModeSim
+
+# -- Boundary 2D simulation setup (RF) ----------------------------------
+sim = BoundaryModeSim()
+sim.set_output_dir(RF_OUTPUT_DIR)
+sim.set_stack(stack)
+sim.set_airbox(**AIRBOX)
+sim.set_geometry(comp)
+
+sim.set_cross_section(f"{CROSS_SECTION_AXIS}={CROSS_SECTION_VALUE}")
+sim.set_boundary_mode(freq=F_RF, num_modes=NUM_RF_MODES, save=2)
+
+# -- Mesh ---------------------------------------------------------------------
+sim.mesh(
+    preset=RF_MESH["preset"],
+    refined_mesh_size=RF_MESH["refined_mesh_size"],
+    max_mesh_size=RF_MESH["max_mesh_size"],
+    fmax=RF_MESH["fmax"],
+    margin_x=MESH_MARGIN_X,
+    margin_y=MESH_MARGIN_Y,
+)
+
+# Show the 2D domain groups created by the solver
+domain_groups = list(sim._last_mesh_result.groups["volumes"].keys())
+print("2D domain groups:", domain_groups)
+sim.print_mesh_stats()
+
+# %%
+# Interactive 3D mesh visualisation
+sim.plot_mesh(
+    transparent_groups=["air__None", "air__passive", "oxide__passive"],
+    style="solid",
+    interactive=True,
+)
+
+# %%
+# Generate Palace config file (mesh must be present)
+sim.add_impedance_boundary("p_rib", "n_rib", capacitance=PN_JUNCTION_CAPACITANCE)
+sim.write_config()
+print("Config written to:", sim.output_dir)
+
+# %%
+# -- RF simulation (50 GHz) ------------------------------------------------
+results = sim.run_local(verbose=True)
+results.print()
+
+# %%
+# --- Post-processing: RF mode fields ---
+import importlib
+
+import gsim.palace.field_viz as field_viz
+import gsim.palace.results as palace_results
+from gsim.palace import plot_fields_2d
+
+importlib.reload(field_viz)
+importlib.reload(palace_results)
+
+if not hasattr(results, "modes"):
+    results = palace_results.load_text_results(RF_OUTPUT_DIR)
+
+results.print()
+
+pl = plot_fields_2d(
+    RF_OUTPUT_DIR,
+    field=RF_FIELD,
+    title=RF_FIELD_TITLE,
+    interactive=True,
+)
+
+# %%
+# --- Rib waveguide zoom: select by physical group names ---
+from gsim.palace import plot_fields_2d
+
+pl = plot_fields_2d(
+    RF_OUTPUT_DIR,
+    field=RF_FIELD,
+    physical_groups=RIB_PHYSICAL_GROUPS,
+    title="RF Mode |E| in the Rib Waveguide (50 GHz, zoomed)",
+    interactive=True,
+)
+
+# %% [markdown]
+# ## Optical simulation (1550 nm)
+#
+# The **simplified optical component** (rib + slab + PN junction, all Si) is
+# analysed at optical frequencies to compute the mode confined in the rib
+# waveguide. It uses the minimal all-dielectric stack with a **uniform SiO2
+# cladding** and **no air**: the padded 2D domain background is set to SiO2 via
+# `set_airbox(material="sio2", ...)` instead of the default air.
+# `run_local()` locates the Palace binary internally — there is no
+# manual `subprocess` / binary-search here.
+#
+# Material dispersion is evaluated at `F_OPT` by the boundary-mode config
+# generator, so the Si and SiO2 domains use their Sellmeier optical constants.
+
+# %%
+# =============================================================================
+#  Optical parameters (1550 nm BoundaryMode run)
+# =============================================================================
+
+F_OPT = 193.4e12  # ~1550 nm
+LAMBDA_OPT = 1.55  # reference wavelength (um)
+NUM_OPT_MODES = 4
+TARGET_INDEX = 2.5
+TOLERANCE = 1e-8
+OPT_OUTPUT_DIR = "./palace-sim-mzm-pn-opt"
+OPT_MESH = {
+    "preset": "default",
+    "refined_mesh_size": 0.2,
+    "max_mesh_size": 0.5,
+}
+
+# Optical post-processing
+OPT_FIELD = "E_real"
+OPT_FIELD_TITLE = "Optical Mode |E| at x=0 (1550 nm)"
+OPT_RIB_PHYSICAL_GROUPS = ["slab", "p_rib", "n_rib"]
+
+
+# %%
+# -- Optical setup + run (1550 nm) ---------------------------------------
+sim_optical = BoundaryModeSim()
+sim_optical.set_output_dir(OPT_OUTPUT_DIR)
+sim_optical.set_stack(stack_opt)
+# Uniform SiO2 cladding: the padded 2D domain is filled with SiO2 (material=
+# "sio2") instead of air, so the device sits in a uniform dielectric background.
+# Only modest padding is needed since the cladding now surrounds the rib
+# directly. The "absorbing boundary on solid dielectric" warning from mesh() is
+# expected here — for an eigenmode cross-section the PML sits far from the mode.
+sim_optical.set_airbox(
+    material="sio2",
+    margin_x=3.0,
+    margin_y=3.0,
+    z_above=3.0,
+    z_below=2.0,
+)
+sim_optical.set_geometry(comp_optical)
+
+sim_optical.set_cross_section(f"{CROSS_SECTION_AXIS}={CROSS_SECTION_VALUE}")
+sim_optical.set_boundary_mode(
+    freq=F_OPT,
+    num_modes=NUM_OPT_MODES,
+    save=2,
+    target=TARGET_INDEX,
+    tolerance=TOLERANCE,
+)
+
+# Optical constants at 1550 nm (Sellmeier). The config generator also resolves
+# dispersion at F_OPT automatically; these overrides keep the config explicit.
+sim_optical.set_material(
+    "si", material_type="dielectric", permittivity=si_opt.permittivity_scalar
+)
+sim_optical.set_material(
+    "sio2", material_type="dielectric", permittivity=sio2_opt.permittivity_scalar
+)
+
+sim_optical.mesh(
+    preset=OPT_MESH["preset"],
+    refined_mesh_size=OPT_MESH["refined_mesh_size"],
+    max_mesh_size=OPT_MESH["max_mesh_size"],
+)
+
+# The optical-only stack has no conductors (only shaped dielectrics), which the
+# default write_config() mesh validation accepts. Generate config.json so the
+# local run below has something to submit.
+sim_optical.write_config()
+
+# %%
+# Interactive 3D mesh visualisation
+sim_optical.plot_mesh(
+    transparent_groups=["air__None", "air__passive", "oxide__passive"],
+    style="solid",
+    interactive=True,
+)
+
+# %%
+opt_results = sim_optical.run_local(verbose=True)
+opt_results.print()
+
+# %%
+# --- Optical mode in the rib waveguide (1550 nm) ---
+from gsim.palace import plot_fields_2d
+
+pl = plot_fields_2d(
+    OPT_OUTPUT_DIR,
+    field=OPT_FIELD,
+    title=OPT_FIELD_TITLE,
+    interactive=True,
+)
+
+# %%
+# --- Rib waveguide zoom: optical physical groups (all Si) ---
+pl = plot_fields_2d(
+    OPT_OUTPUT_DIR,
+    field=OPT_FIELD,
+    physical_groups=OPT_RIB_PHYSICAL_GROUPS,
+    title="Optical Mode |E| in the Rib Waveguide (1550 nm, zoomed)",
+    interactive=True,
+)
+
+# %% [markdown]
+# ## Summary
+#
+# The geometry has been built and meshed for both RF (50 GHz) and optical (193 THz / 1550 nm) analysis.
+#
+# **Cross-section elements:**
+# | Component | Layer | y-range (um) | z-range (um) | Material | sigma (S/m) |
+# |---|---|---|---|---|---|
+# | Rib core | WG (1,0) | [-20.2, -19.8] | [0, 0.22] | Si (intrinsic) | 2 |
+# | Slab (90 nm) | SLAB90 (3,0) | [-40.2, +0.2] | [0, 0.09] | Si (intrinsic) | 2 |
+# | PN junction (P) | P (21,0) | [-20.0, -19.8] | [0, 0.22] | doped Si (p_rib) | 1.6x10^3 |
+# | PN junction (N) | N (20,0) | [-20.2, -20.0] | [0, 0.22] | doped Si (n_rib) | 1.6x10^3 |
+# | P+ graded inner | PP (23,0) | [-18.3, -16.3] | [0, 0.09] | doped Si (pp_slab_0) | 2x10^4 |
+# | P+ graded outer | PP (23,1) | [-15.3, -13.3] | [0, 0.09] | doped Si (pp_slab_1) | 8x10^4 |
+# | N+ graded inner | NPP (24,0) | [-21.7, -23.7] | [0, 0.09] | doped Si (npp_slab_0) | 2x10^4 |
+# | N+ graded outer | NPP (24,1) | [-24.7, -26.7] | [0, 0.09] | doped Si (npp_slab_1) | 8x10^4 |
+# | Vias (S to P+) | VIAC/VIA1/VIA2 | [-15.0, -9.0] | [0.09, 3.2] | W/Al | 3.5x10^7 |
+# | Vias (G to N+) | VIAC/VIA1/VIA2 | [-31.0, -25.0] | [0.09, 3.2] | W/Al | 3.5x10^7 |
+# | CPW signal | M1 (41,0) | [-10, +10] | [3.2, 4.2] | Al (1 um) | 3.5x10^7 |
+# | CPW ground (top) | M1 (41,0) | [+30, +70] | [3.2, 4.2] | Al (1 um) | 3.5x10^7 |
+# | CPW ground (bot) | M1 (41,0) | [-70, -30] | [3.2, 4.2] | Al (1 um) | 3.5x10^7 |
+#
+# **Material modelling notes:**
+# - Doping regions are modelled as **semiconductors** (finite sigma from the Drude free-carrier model), not metals. This avoids short-circuiting the PN junction.
+# - Conductivities are derived from $\sigma = q\mu N$ with typical dopant concentrations ($N \sim 10^{19}\ \text{cm}^{-3}$ for the junction, $\sim 10^{20}\ \text{cm}^{-3}$ for the contacts).
+# - Doping on each side of the rib uses a **configurable piecewise gradient** via `make_doping_profile()`, and the whole cross-section assembly is wrapped by `build_doped_cross_section()`.
+# - The **depletion region** and voltage-dependent capacitance are NOT modelled here — this is a linear small-signal analysis at a fixed bias point.
+# - The **plasma-dispersion effect** is not applied to the optical simulation; the rib is treated as intrinsic Si at 1550 nm.
+#
+# **Optical-only component:**
+# - The optical run (`sim_optical`) uses a **simplified component** — the same
+#   rib + slab + PN junction ("doping profile") polygons, but no electrodes,
+#   vias, or graded doping.
+# - Every device region maps to **plain silicon** in `build_optical_cross_section()`,
+#   so the optical mode sees one homogeneous Si body in a **uniform SiO2 cladding**.
+# - The background medium is SiO2, not air: `set_airbox(material="sio2", ...)`
+#   fills the padded 2D domain with the cladding material (default is air).
+# - Material dispersion is evaluated at `F_OPT` by the boundary-mode config
+#   generator: Si -> eps~12.09 (n~3.478), SiO2 -> eps~2.09 (n~1.444) at 1550 nm.
+#
+# **Next steps (user action):**
+# 1. Verify the zoomed cross-section plot shows the rib (centred at y=-20), PN junction, graded doping, and vias.
+# 2. Run `sim.run_local(verbose=True)` with a Palace CPU runner installed (`pip install gsim[palace-toolkit-cpu]`). 2D
+#    mode analysis defaults to a single MPI rank + OpenMP threads; pass `num_processes=1` explicitly if you want
+#    to be explicit about it.
+# 3. Run `sim_optical.run_local(verbose=True)` for the optical mode.
+# 4. Use `gsim.palace.plot_fields_2d()` to visualise mode profiles, and `gsim.palace.plot_plane_section()` for cross-section physical groups.
+#
+
+# %%
+# Quick verification: dump the 2D cross-section layer regions
+print("=== RF cross-section regions (x=0) ===")
+for r in section:
+    print(
+        f"  {r.layer_name:12s}  mat={r.material:10s}  "
+        f"y=[{r.y0:6.2f},{r.y1:6.2f}]  z=[{r.zmin:5.3f},{r.zmax:5.3f}]"
+    )
+print("\n=== Optical cross-section regions (x=0) ===")
+for r in section_opt:
+    print(
+        f"  {r.layer_name:12s}  mat={r.material:10s}  "
+        f"y=[{r.y0:6.2f},{r.y1:6.2f}]  z=[{r.zmin:5.3f},{r.zmax:5.3f}]"
+    )
diff --git a/output/palace/palace.json b/output/palace/palace.json
new file mode 100644
index 00000000..f8bff13c
--- /dev/null
+++ b/output/palace/palace.json
@@ -0,0 +1,7 @@
+{
+  "GitTag": "v0.16.1-51-g4f2e2d97",
+  "Problem": {
+    "MPISize": 4,
+    "OpenMPThreads": 1
+  }
+}
diff --git a/pyproject.toml b/pyproject.toml
index f6cdd311..13035258 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -31,7 +31,19 @@ dependencies = [
 # GitHub Releases. Currently only Linux x86_64 wheels are available, so
 # the extra is platform-marked accordingly.
 palace-toolkit-cpu = [
-  "palacetoolkit-palace-cpu @ https://github.com/EpsilonForge/PalaceToolkit/releases/download/palace-cpu-v0.1.2/palacetoolkit_palace_cpu-0.1.0-py3-none-linux_x86_64.whl ; sys_platform == 'linux' and platform_machine == 'x86_64'",
+  "palacetoolkit-palace-cpu @ https://github.com/EpsilonForge/PalaceToolkit/releases/download/palace-cpu-v0.17.0/palacetoolkit_palace_cpu-0.17.0-py3-none-linux_x86_64.whl ; sys_platform == 'linux' and platform_machine == 'x86_64'",
+]
+# Interactive 3-D visualization (PyVista + trame server rendering) with the
+# extra packages needed for reliable headless and notebook use.
+visualize = [
+  "jupyter-server-proxy>=4.1.0",
+  "nest-asyncio",
+  "pyvirtualdisplay>=3.0.0",
+  "trame>=3.6.0,<4",
+  "trame-client>=3.6.0,<4",
+  "trame-server>=3.6.0,<4",
+  "trame-vtk>=2.8.0,<3",
+  "trame-vuetify>=2.7.0,<3",
 ]
 
 [dependency-groups]
diff --git a/src/gsim/common/cross_section.py b/src/gsim/common/cross_section.py
index 133c46b3..170d38e5 100644
--- a/src/gsim/common/cross_section.py
+++ b/src/gsim/common/cross_section.py
@@ -11,15 +11,16 @@
 from __future__ import annotations
 
 import logging
+from collections.abc import Iterable, Mapping
 from dataclasses import dataclass
-from typing import TYPE_CHECKING, Literal, overload
+from typing import TYPE_CHECKING, Any, Literal, overload
 
-logger = logging.getLogger(__name__)
+from gsim.common.stack import Layer, LayerStack, get_stack, make_doped_materials
 
 if TYPE_CHECKING:
     import gdsfactory as gf
 
-    from gsim.common.stack import LayerStack
+logger = logging.getLogger(__name__)
 
 
 @dataclass(frozen=True)
@@ -213,6 +214,253 @@ def extract_plane_section(
     )
 
 
+def build_doped_cross_section(
+    component: gf.Component,
+    *,
+    axis: Literal["x", "y", "z"],
+    value: float,
+    substrate_thickness: float,
+    include_substrate: bool = False,
+    doping: Mapping[str, Mapping[str, Any]] | None = None,
+    metal1: tuple[float, float] | None = None,
+    rib_layers: Iterable[tuple[str, tuple[int, int], float]] = (),
+    rib_height: float = 0.22,
+    permittivity: float = 11.9,
+    fmax: float = 200e9,
+    verbose: bool = True,
+) -> tuple[LayerStack, list[Rect2D] | list[RectYZ2D] | list[PolygonXY2D]]:
+    """Assemble a doped ``LayerStack`` and extract a 2D plane section from it.
+
+    Builds the base PDK stack, optionally overrides the ``metal1`` electrodes,
+    registers the gradient-doping layers/materials produced by
+    :func:`gsim.common.stack.doping.make_doping_profile` plus any additional rib
+    doping layers (e.g. a PN junction), and slices the component at the requested
+    plane.
+
+    Args:
+        component: gdsfactory component the cross-section is extracted from.
+        axis: Cross-section normal axis.
+        value: Plane coordinate in um.
+        substrate_thickness: Thickness below z=0 in um.
+        include_substrate: Include the lossy silicon substrate.
+        doping: Output of ``make_doping_profile`` (keys ``layer_specs`` and
+            ``materials``), or ``None`` to skip gradient doping.
+        metal1: ``(zmin, thickness)`` override for the ``metal1`` layer, or
+            ``None`` to keep the PDK value.
+        rib_layers: Sequence of ``(name, gds_layer, sigma)`` for extra rib doping
+            regions (e.g. PN junction) added on top of the gradient profile.
+        rib_height: Z-extent (z=0..rib_height) of the rib doping regions (um).
+        permittivity: Relative permittivity of the doping materials.
+        fmax: Upper frequency of the doping dispersion-model validity (Hz).
+        verbose: Print the assembled stack and the extracted section.
+
+    Returns:
+        ``(stack, section)`` with the populated ``LayerStack`` and the list of
+        ``Rect2D`` / ``RectYZ2D`` / ``PolygonXY2D`` regions at the plane.
+    """
+    stack = get_stack(
+        substrate_thickness=substrate_thickness,
+        include_substrate=include_substrate,
+    )
+
+    if metal1 is not None:
+        metal1_zmin, metal1_thickness = metal1
+        m1 = stack.layers.get("metal1")
+        if m1:
+            m1.zmin = metal1_zmin
+            m1.zmax = metal1_zmin + metal1_thickness
+            m1.thickness = metal1_thickness
+            if verbose:
+                logger.info(
+                    "M1 updated: zmin=%s, zmax=%s, thickness=%s",
+                    m1.zmin,
+                    m1.zmax,
+                    m1.thickness,
+                )
+
+    layer_specs: dict[str, Any] = {}
+    materials: dict[str, Any] = {}
+    if doping:
+        layer_specs.update(doping.get("layer_specs", {}))
+        materials.update(doping.get("materials", {}))
+
+    rib_materials = make_doped_materials(
+        [(name, sigma) for name, _gds, sigma in rib_layers],
+        permittivity=permittivity,
+        fmax=fmax,
+    )
+    materials.update(rib_materials)
+    for name, gds_layer, _sigma in rib_layers:
+        layer_specs[name] = Layer(
+            name=name,
+            gds_layer=gds_layer,
+            zmin=0.0,
+            zmax=rib_height,
+            thickness=rib_height,
+            material=name,
+            layer_type="dielectric",
+            mesh_resolution="fine",
+        )
+
+    for name, layer in layer_specs.items():
+        stack.layers[name] = layer
+
+    section = extract_plane_section(
+        component.copy(),
+        stack,
+        axis=axis,
+        value=value,
+    )
+
+    if verbose:
+        logger.info("Stack: %s", stack.pdk_name)
+        logger.info("Layers: %s", sorted(stack.layers.keys()))
+        logger.info("Cross materials: %s", sorted(materials.keys()))
+        logger.info("Dielectrics: %s", stack.dielectrics)
+        logger.info("")
+        logger.info(
+            "Cross-section %s=%s intersects %s layer regions:",
+            axis,
+            value,
+            len(section),
+        )
+        for r in section:
+            lo = getattr(r, "y0", getattr(r, "x0", None))
+            hi = getattr(r, "y1", getattr(r, "x1", None))
+            zlo = getattr(r, "zmin", None)
+            zhi = getattr(r, "zmax", None)
+            if zlo is None:
+                logger.info("  %-12s material=%-10s", r.layer_name, r.material)
+            else:
+                logger.info(
+                    "  %-12s material=%-10s y=[%8.3f, %8.3f]  z=[%6.3f, %6.3f]",
+                    r.layer_name,
+                    r.material,
+                    lo,
+                    hi,
+                    zlo,
+                    zhi,
+                )
+
+    return stack, section
+
+
+def build_optical_cross_section(
+    component: gf.Component,
+    *,
+    axis: Literal["x", "y", "z"],
+    value: float,
+    device_layers: Mapping[str, tuple[tuple[int, int], float, float]],
+    substrate_thickness: float = 2.0,
+    cladding_top: float = 2.0,
+    device_material: str = "si",
+    cladding_material: str = "sio2",
+    mesh_resolution: str | float = "fine",
+    verbose: bool = True,
+) -> tuple[LayerStack, list[Rect2D] | list[RectYZ2D] | list[PolygonXY2D]]:
+    """Assemble a minimal all-dielectric ``LayerStack`` and extract a plane section.
+
+    Builds a photonic ``LayerStack`` for a simplified device — e.g. a rib +
+    slab + PN junction made of a single semiconductor — sitting in a uniform
+    cladding background. Unlike :func:`build_doped_cross_section`, every device
+    region is mapped to the same plain dielectric material (e.g. ``"si"``) and
+    no electrodes, vias, or graded doping are registered. A single ``oxide``
+    dielectric slab (the cladding material) spans the full stack z-range, so the
+    simulation domain is a uniform cladding with only the drawn device embedded
+    in it.
+
+    Args:
+        component: gdsfactory component the cross-section is extracted from.
+        axis: Cross-section normal axis.
+        value: Plane coordinate in um.
+        device_layers: Mapping of ``name -> (gds_layer, zmin, zmax)`` for every
+            patterned device region (e.g. ``{"core": ((1, 0), 0.0, 0.22)}``).
+            All regions share ``device_material``.
+        substrate_thickness: Cladding thickness below z=0 in um.
+        cladding_top: Cladding thickness above z=0 in um.
+        device_material: Material name for all device regions (default ``"si"``).
+        cladding_material: Material name of the uniform background (default
+            ``"sio2"``).
+        mesh_resolution: Mesh resolution assigned to the device ``Layer`` specs.
+        verbose: Print the assembled stack and the extracted section.
+
+    Returns:
+        ``(stack, section)`` with the populated ``LayerStack`` (device layers +
+        uniform cladding dielectric + materials) and the list of ``Rect2D`` /
+        ``RectYZ2D`` / ``PolygonXY2D`` regions at the plane.
+    """
+    from gsim.common.stack.extractor import Layer, LayerStack
+    from gsim.common.stack.materials import get_material_properties
+
+    stack = LayerStack(pdk_name="optical")
+
+    for name, (gds_layer, zmin, zmax) in device_layers.items():
+        stack.layers[name] = Layer(
+            name=name,
+            gds_layer=gds_layer,
+            zmin=zmin,
+            zmax=zmax,
+            thickness=zmax - zmin,
+            material=device_material,
+            layer_type="dielectric",
+            mesh_resolution=mesh_resolution,
+        )
+
+    stack.dielectrics.append(
+        {
+            "name": "oxide",
+            "zmin": -substrate_thickness,
+            "zmax": cladding_top,
+            "material": cladding_material,
+        }
+    )
+
+    for material in (device_material, cladding_material):
+        props = get_material_properties(material)
+        if props is not None:
+            stack.materials[material] = props.to_dict()
+
+    section = extract_plane_section(
+        component.copy(),
+        stack,
+        axis=axis,
+        value=value,
+    )
+
+    if verbose:
+        logger.info("Stack: %s", stack.pdk_name)
+        logger.info("Layers: %s", sorted(stack.layers.keys()))
+        logger.info("Device material: %s", device_material)
+        logger.info("Cladding material: %s", cladding_material)
+        logger.info("Dielectrics: %s", stack.dielectrics)
+        logger.info("")
+        logger.info(
+            "Cross-section %s=%s intersects %s layer regions:",
+            axis,
+            value,
+            len(section),
+        )
+        for r in section:
+            lo = getattr(r, "y0", getattr(r, "x0", None))
+            hi = getattr(r, "y1", getattr(r, "x1", None))
+            zlo = getattr(r, "zmin", None)
+            zhi = getattr(r, "zmax", None)
+            if zlo is None:
+                logger.info("  %-12s material=%-10s", r.layer_name, r.material)
+            else:
+                logger.info(
+                    "  %-12s material=%-10s y=[%8.3f, %8.3f]  z=[%6.3f, %6.3f]",
+                    r.layer_name,
+                    r.material,
+                    lo,
+                    hi,
+                    zlo,
+                    zhi,
+                )
+
+    return stack, section
+
+
 @overload
 def _extract_line_slice_rectangles(
     component,
@@ -436,6 +684,8 @@ def _line_intervals(
     "PolygonXY2D",
     "Rect2D",
     "RectYZ2D",
+    "build_doped_cross_section",
+    "build_optical_cross_section",
     "extract_plane_section",
     "extract_xy_polygons",
     "extract_xz_rectangles",
diff --git a/src/gsim/common/stack/__init__.py b/src/gsim/common/stack/__init__.py
index 6bc85ec7..57bcd5c5 100644
--- a/src/gsim/common/stack/__init__.py
+++ b/src/gsim/common/stack/__init__.py
@@ -23,6 +23,7 @@
 import gdsfactory as gf
 import yaml
 
+from gsim.common.stack.doping import make_doping_profile
 from gsim.common.stack.extractor import (
     Layer,
     LayerStack,
@@ -39,6 +40,8 @@
     SellmeierTerm,
     ValidityRange,
     get_material_properties,
+    make_doped_material,
+    make_doped_materials,
     resolve_material_at_wavelength,
     should_enable_dispersion,
 )
@@ -180,6 +183,9 @@ def load_stack_yaml(yaml_path: str | Path) -> LayerStack:
     "get_stack",
     "load_overlay",
     "load_stack_yaml",
+    "make_doped_material",
+    "make_doped_materials",
+    "make_doping_profile",
     "merge_overlay",
     "parse_layer_stack",
     "plot_stack",
diff --git a/src/gsim/common/stack/doping.py b/src/gsim/common/stack/doping.py
new file mode 100644
index 00000000..51de63c8
--- /dev/null
+++ b/src/gsim/common/stack/doping.py
@@ -0,0 +1,166 @@
+"""Doping-profile construction for semiconductor cross-sections.
+
+This module provides solver-agnostic helpers to build contiguous (gapless)
+doping regions on both sides of a rib/waveguide and to generate the
+corresponding ``Layer`` specs (``gsim.common.stack.extractor``) and
+``MaterialProperties`` (``gsim.common.stack.materials``).
+
+All geometry-specific values (layer tuples, naming prefixes, doping widths,
+conductivities, z-extents) are caller-supplied — nothing is hardcoded here so
+the helpers are reusable across PDKs and processes.
+
+Example:
+-------
+    >>> import gdsfactory as gf
+    >>> from gsim.common.stack.doping import make_doping_profile
+    >>> comp = gf.Component()
+    >>> result = make_doping_profile(
+    ...     comp,
+    ...     length=10.0,
+    ...     rib_center_y=-20.0,
+    ...     rib_width=0.4,
+    ...     profile={
+    ...         "upper": [(2.0, 2e4), (2.0, 8e4)],
+    ...         "lower": [(2.0, 2e4), (2.0, 8e4)],
+    ...     },
+    ...     sides={
+    ...         "upper": {"base_layer": (23, 0), "name_prefix": "pp_slab_", "sign": 1},
+    ...         "lower": {
+    ...             "base_layer": (24, 0),
+    ...             "name_prefix": "npp_slab_",
+    ...             "sign": -1,
+    ...         },
+    ...     },
+    ...     zmin=0.0,
+    ...     zmax=0.09,
+    ... )
+    >>> result["layer_specs"]
+    >>> result["materials"]
+    >>> result["centres"]
+"""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, Any, cast
+
+import gdsfactory as gf
+
+from gsim.common.stack.materials import make_doped_materials
+
+if TYPE_CHECKING:
+    from gsim.common.stack.extractor import Layer
+
+_SideConfig = dict[str, dict[str, Any]]
+
+
+def make_doping_profile(
+    comp: gf.Component,
+    *,
+    length: float,
+    rib_center_y: float,
+    rib_width: float,
+    profile: dict[str, list[tuple[float, float]]],
+    sides: _SideConfig,
+    zmin: float,
+    zmax: float,
+    permittivity: float = 11.9,
+    fmax: float = 200e9,
+    mesh_resolution: str | float = "fine",
+) -> dict[str, dict[str, Any]]:
+    """Add contiguous doping regions beside a rib and build layer/material specs.
+
+    For each side (e.g. ``"upper"`` / ``"lower"``) the regions listed in
+    *profile* are placed as adjacent rectangles starting at the rib edge and
+    extending outward, so the doping is contiguous with no gaps.  Each region
+    ``i`` on a side gets:
+
+    - a gdsfactory rectangle of size ``(length, width)`` on the GDS layer
+      ``(base_layer[0], base_layer[1] + i)``,
+    - a ``Layer`` spec named ``"{name_prefix}{i}"``,
+    - a ``MaterialProperties`` entry with the region's Drude conductivity.
+
+    Args:
+        comp: gdsfactory component the rectangles are added to.
+        length: Rectangle length along the propagation direction (um).
+        rib_center_y: Y coordinate of the rib centre (um).
+        rib_width: Rib width (um); regions start at the rib edges.
+        profile: Per-side region list ``{side: [(width_um, sigma_S_per_m), ...]}``.
+        sides: Per-side configuration: each value is a dict with keys
+            ``base_layer`` (``(layer, datatype)`` tuple for the first region),
+            ``name_prefix`` (region-name prefix) and ``sign`` (+1 extends in
+            +y, -1 in -y).
+        zmin: Bottom z of the doping regions (um).
+        zmax: Top z of the doping regions (um).
+        permittivity: Relative permittivity shared by all regions (e.g. 11.9).
+        fmax: Upper frequency of the dispersion-model validity range (Hz).
+        mesh_resolution: Mesh resolution assigned to the generated ``Layer``.
+
+    Returns:
+        Dict with keys ``layer_specs`` (``{name: Layer}``), ``materials``
+        (``{name: MaterialProperties}``) and ``centres``
+        (``{side: [y_centre, ...]}``).
+    """
+    from gsim.common.stack.extractor import Layer
+
+    result: dict[str, dict[str, Any]] = {
+        "layer_specs": {},
+        "materials": {},
+        "centres": {},
+    }
+    layer_specs = cast("dict[str, Layer]", result["layer_specs"])
+    materials: dict[str, Any] = result["materials"]
+    centres: dict[str, list[float]] = result["centres"]
+
+    for side, cfg in sides.items():
+        regions = profile.get(side, [])
+        sign = cfg["sign"]
+        base_layer = tuple(cfg["base_layer"])
+        prefix = cfg["name_prefix"]
+
+        pos = rib_center_y + sign * rib_width / 2  # start at rib edge
+        side_centres: list[float] = []
+        side_specs: dict[str, tuple[Any, float]] = {}
+
+        for i, (width, sigma) in enumerate(regions):
+            name = f"{prefix}{i}"
+            gds_layer = (base_layer[0], base_layer[1] + i)
+            centre = pos + sign * width / 2
+
+            rect = comp << gf.c.rectangle((length, width), layer=gds_layer)
+            rect.y = centre
+            side_centres.append(centre)
+            side_specs[name] = (gds_layer, sigma)
+            pos += sign * width
+
+        centres[side] = side_centres
+        if not side_specs:
+            continue
+
+        layer_specs.update(
+            {
+                name: Layer(
+                    name=name,
+                    gds_layer=gds_layer,
+                    zmin=zmin,
+                    zmax=zmax,
+                    thickness=zmax - zmin,
+                    material=name,
+                    layer_type="dielectric",
+                    mesh_resolution=mesh_resolution,
+                )
+                for name, (gds_layer, _sigma) in side_specs.items()
+            }
+        )
+        materials.update(
+            make_doped_materials(
+                [(name, sigma) for name, (_gds, sigma) in side_specs.items()],
+                permittivity=permittivity,
+                fmax=fmax,
+                source_prefix="doped Si",
+            )
+        )
+
+    return result
+
+
+__all__ = ["make_doping_profile"]
diff --git a/src/gsim/common/stack/materials.py b/src/gsim/common/stack/materials.py
index bbba49bd..2a619a88 100644
--- a/src/gsim/common/stack/materials.py
+++ b/src/gsim/common/stack/materials.py
@@ -24,7 +24,8 @@
 
 import math
 import warnings
-from typing import Literal
+from collections.abc import Iterable
+from typing import Literal, cast
 
 from pydantic import BaseModel, ConfigDict, Field
 from scipy.constants import c as C0  # noqa: N812
@@ -576,6 +577,119 @@ def dielectric(
         return cls(permittivity=permittivity, loss_tangent=loss_tangent)
 
 
+def make_doped_material(
+    name: str,
+    conductivity: float,
+    *,
+    permittivity: float = 11.9,
+    fmax: float = 200e9,
+    source: str | None = None,
+) -> MaterialProperties:
+    """Create ``MaterialProperties`` for a doped semiconductor.
+
+    Doped silicon (and similar semiconductors) are modelled with a finite
+    Drude conductivity ``sigma`` and a constant relative permittivity that
+    is valid up to ``fmax`` (in Hz).  This is the building block used by
+    :func:`make_doped_materials` and the doping-profile helpers.
+
+    Args:
+        name: Material name (used to label the dispersion-model source).
+        conductivity: DC conductivity in S/m (e.g. from ``sigma = q*mu*N``).
+        permittivity: Relative permittivity (default: 11.9 for silicon).
+        fmax: Upper frequency of the validity range in Hz.
+        source: Optional citation/source string.  Defaults to
+            ``"doped Si ({name}) -- Drude sigma"``.
+
+    Returns:
+        A ``MaterialProperties`` instance with a constant dispersion model.
+    """
+    source = source or f"doped Si ({name}) -- Drude sigma"
+    return MaterialProperties(
+        permittivity=permittivity,
+        conductivity=conductivity,
+        dispersion_models=[
+            DispersionModel(
+                type="constant",
+                permittivity=permittivity,
+                validity=ValidityRange(valid_frequency=(0, fmax)),
+                source=source,
+            )
+        ],
+    )
+
+
+def make_doped_materials(
+    entries: (
+        dict[str, float]
+        | Iterable[tuple[str, float]]
+        | Iterable[tuple[str, float, float, str]]
+    ),
+    *,
+    permittivity: float = 11.9,
+    fmax: float = 200e9,
+    source_prefix: str = "doped Si",
+) -> dict[str, MaterialProperties]:
+    """Create a dict of doped-material ``MaterialProperties``.
+
+    Each entry describes one doping region and is either a ``(name, sigma)``
+    pair (using the shared *permittivity* / *fmax*) or a 4-tuple
+    ``(name, permittivity, sigma, source)`` for full control.
+
+    Args:
+        entries: ``{name: sigma}`` dict, ``[(name, sigma), ...]`` list, or
+            ``[(name, permittivity, sigma, source), ...]`` list.
+        permittivity: Relative permittivity for 2-tuple entries.
+        fmax: Upper validity frequency in Hz for 2-tuple entries.
+        source_prefix: Source label prefix for 2-tuple entries.
+
+    Returns:
+        Dict mapping each name to a ``MaterialProperties`` instance.
+
+    Examples:
+        >>> make_doped_materials({"pp_slab_0": 2e4, "pp_slab_1": 8e4})
+        >>> make_doped_materials([("p_rib", 11.9, 1.6e3, "junction")])
+    """
+    items: list[tuple[str, float, float, str]] = []
+
+    if isinstance(entries, dict):
+        for name, sigma in cast(dict[str, float], entries).items():
+            items.append(
+                (name, permittivity, sigma, f"{source_prefix} ({name}) -- Drude sigma")
+            )
+    else:
+        for entry in entries:
+            if len(entry) == 2:
+                name, sigma = entry  # type: ignore[arg-type]
+                items.append(
+                    (
+                        name,
+                        permittivity,
+                        sigma,
+                        f"{source_prefix} ({name}) -- Drude sigma",
+                    )
+                )
+            elif len(entry) == 4:
+                items.append(entry)  # type: ignore[arg-type]
+            else:
+                msg = (
+                    "Entries must be (name, sigma) or (name, permittivity, "
+                    f"sigma, source) tuples, got {entry!r}"
+                )
+                raise ValueError(msg)
+
+    materials: dict[str, MaterialProperties] = {}
+    for name, eps, sigma, source in items:
+        materials[name] = make_doped_material(
+            name,
+            sigma,
+            permittivity=eps,
+            fmax=fmax,
+            source=source,
+        )
+
+    return materials
+
+
 MATERIALS_DB: dict[str, MaterialProperties] = {
     "aluminum": MaterialProperties(
         conductivity=3.77e7,
diff --git a/src/gsim/palace/__init__.py b/src/gsim/palace/__init__.py
index 3009ebbc..836c67cd 100644
--- a/src/gsim/palace/__init__.py
+++ b/src/gsim/palace/__init__.py
@@ -59,6 +59,9 @@
 from gsim.palace.eigenmode import EigenmodeSim
 from gsim.palace.electrostatic import ElectrostaticSim
 
+# Visualization
+from gsim.palace.field_viz import plot_fields_2d, resolve_physical_groups
+
 # Field-visualization (NaN-free direct mesh rendering)
 from gsim.palace.fields import (
     BoundaryFieldData,
@@ -111,6 +114,7 @@
     ValidationResult,
     WavePortConfig,
 )
+from gsim.palace.plane_section import plot_plane_section
 
 # Port utilities
 from gsim.palace.ports import (
@@ -134,9 +138,15 @@
 
 # Runtime / binary resolution (optional palace-toolkit-cpu dependency)
 from gsim.palace.runtime import resolve_palace_binary, resolve_palace_library_dir
-
-# Visualization
-from gsim.viz import plot_cross_section, plot_mesh
+from gsim.viz import (
+    close_interactive_view,
+    close_interactive_views,
+    interactive_mode,
+    plot_cross_section,
+    plot_mesh,
+    set_interactive_mode,
+    set_trame_backend,
+)
 
 __all__ = [
     "MATERIALS_DB",
@@ -179,6 +189,8 @@
     "WavePortConfig",
     "activate_vector_component",
     "build_selector_context",
+    "close_interactive_view",
+    "close_interactive_views",
     "configure_cpw_port",
     "configure_inplane_port",
     "configure_via_port",
@@ -194,6 +206,7 @@
     "get_material_properties",
     "get_port_map",
     "get_stack",
+    "interactive_mode",
     "load_boundary_field_data",
     "load_field_context",
     "load_fields",
@@ -205,6 +218,7 @@
     "plot_cross_section",
     "plot_fields_2d",
     "plot_mesh",
+    "plot_plane_section",
     "plot_stack",
     "plot_volume_contours",
     "plot_volume_slice",
@@ -216,8 +230,11 @@
     "resolve_palace_binary",
     "resolve_palace_library_dir",
     "resolve_palace_materials_at_frequency",
+    "resolve_physical_groups",
     "resolve_scalar_field",
     "run_simulation",
+    "set_interactive_mode",
+    "set_trame_backend",
 ]
 
 
diff --git a/src/gsim/palace/base.py b/src/gsim/palace/base.py
index 33bb6b2e..d64ca3e2 100644
--- a/src/gsim/palace/base.py
+++ b/src/gsim/palace/base.py
@@ -8,6 +8,7 @@
 
 import logging
 import math
+import os
 import tempfile
 from pathlib import Path
 from typing import TYPE_CHECKING, Any, Literal
@@ -16,6 +17,7 @@
     CPWPortConfig,
     DrivenConfig,
     EigenmodeConfig,
+    ImpedanceBoundaryConfig,
     MaterialConfig,
     MeshConfig,
     NumericalConfig,
@@ -34,6 +36,113 @@
 logger = logging.getLogger(__name__)
 
 
+def _count_physical_cpus() -> int:
+    """Return the number of physical CPU cores (not logical threads)."""
+    try:
+        with open("/proc/cpuinfo") as f:
+            content = f.read()
+        # Each physical core has a unique (physical_id, core_id) pair.
+        cores: set[tuple[str, str]] = set()
+        phys_id = None
+        for line in content.splitlines():
+            if line.startswith("physical id"):
+                phys_id = line.split(":")[1].strip()
+            elif line.startswith("core id"):
+                core_id = line.split(":")[1].strip()
+                if phys_id is not None:
+                    cores.add((phys_id, core_id))
+        if cores:
+            return len(cores)
+    except Exception:
+        pass
+    return os.cpu_count() or 1
+
+
+# Minimum estimated unknowns per MPI rank for SuperLU_DIST to factor
+# efficiently. Below this, the 2D block-cyclic processor grid is dominated by
+# communication/fill overhead and the factorization degrades dramatically
+# (an effective hang on small 2D meshes at 8-16 ranks).
+_MIN_DOFS_PER_RANK = 50_000
+# Absolute ceiling on MPI ranks for 3D problems that use a sparse direct
+# solver. 2D (BoundaryMode) problems never use MPI: see _recommend_parallel.
+_MAX_DIRECT_SOLVE_RANKS = 4
+
+
+def _estimate_dofs(mesh_stats: dict) -> int | None:
+    """Estimate total unknowns from mesh statistics.
+
+    Uses the same element-count * polynomial-order heuristic as
+    :meth:`PalaceSimMixin.print_mesh_stats` (order 2 for 2D, 1 for 3D).
+    """
+    if not mesh_stats:
+        return None
+    elements = mesh_stats.get("elements") or 0
+    if not elements:
+        return None
+    is_3d = bool(mesh_stats.get("tetrahedra"))
+    p = 1 if is_3d else 2
+    nd_dofs = elements * p * (p + 1)
+    h1_dofs = elements * (p + 1) * (p + 2) // 2
+    return nd_dofs + h1_dofs
+
+
+def _recommend_parallel(
+    mesh_stats: dict,
+    simulation_type: str,
+    num_processes: int | None,
+    num_threads: int | None,
+    physical_cpus: int | None = None,
+) -> tuple[int, int | None]:
+    """Recommend MPI/OpenMP settings that avoid pathological direct solves.
+
+    SuperLU_DIST factors the MPI rank count into a 2D processor grid. For
+    small problems (especially 2D mode analysis), using every physical core
+    produces a grid (e.g. 4x4 at 16 ranks) whose factorization is
+    communication-bound and effectively hangs. This returns a safe default:
+
+    - 2D (``boundarymode`` or a planar mesh): a single MPI rank with OpenMP
+      threads. MPI for a 2D problem is overkill and the sparse-direct grid
+      does not scale.
+    - 3D: at most ``_MAX_DIRECT_SOLVE_RANKS`` ranks, and never more than
+      ``est_dofs // _MIN_DOFS_PER_RANK`` so each rank has enough unknowns.
+
+    Explicit caller-supplied values are always respected; when they exceed
+    the recommendation the caller should log a warning.
+
+    Returns:
+        ``(num_processes, num_threads)``. ``num_threads`` stays ``None``
+        unless it should be auto-defaulted to the physical core count.
+    """
+    if physical_cpus is None:
+        physical_cpus = _count_physical_cpus()
+
+    if num_processes is not None:
+        # Explicit request: keep it, default threads only for serial runs.
+        if num_processes == 1 and num_threads is None:
+            return num_processes, physical_cpus
+        return num_processes, num_threads
+
+    is_2d = simulation_type == "boundarymode"
+    if not is_2d and mesh_stats:
+        bbox = mesh_stats.get("bbox") or {}
+        dz = bbox.get("zmax", bbox.get("zmin", 0.0)) - bbox.get(
+            "zmin", bbox.get("zmax", 0.0)
+        )
+        if not mesh_stats.get("tetrahedra") and dz <= 1e-6:
+            is_2d = True
+
+    if is_2d:
+        return 1, (num_threads if num_threads is not None else physical_cpus)
+
+    # 3D: size-aware cap for sparse-direct solves.
+    est_dofs = _estimate_dofs(mesh_stats)
+    size_cap = physical_cpus
+    if est_dofs is not None:
+        size_cap = max(1, est_dofs // _MIN_DOFS_PER_RANK)
+    recommended = min(physical_cpus, _MAX_DIRECT_SOLVE_RANKS, size_cap)
+    return max(1, recommended), num_threads
+
+
 class PalaceSimMixin:
     """Mixin providing common methods for all Palace simulation classes.
 
@@ -62,8 +171,9 @@ class PalaceSimMixin:
     _stack_kwargs: dict[str, Any]
     _pec_blocks: list
     _hints: dict[str, Any]
+    _impedance_boundaries: list[ImpedanceBoundaryConfig]
     absorbing_boundary: bool
-    _airbox_config: dict[str, float]
+    _airbox_config: dict[str, Any]
 
     # -------------------------------------------------------------------------
     # Output directory
@@ -192,6 +302,7 @@ def set_airbox(
         margin_y: float | None = None,
         z_above: float | None = None,
         z_below: float | None = None,
+        material: str = "air",
     ) -> None:
         """Configure an explicit weak-priority airbox for meshing.
 
@@ -200,6 +311,17 @@ def set_airbox(
         The resulting airbox is created as a dedicated dielectric volume
         with the weakest boolean-priority in mesh construction.
 
+        ``material`` sets the material name of the padded background region.
+        It defaults to ``"air"`` (eps=1). For a photonic cross-section with a
+        uniform cladding, pass e.g. ``"sio2"`` so the region around the device
+        is filled with SiO2 instead of air. The material must be resolvable in
+        the stack's materials (or the built-in database); its permittivity is
+        evaluated at the simulation frequency (e.g. Sellmeier SiO2 at 1550 nm).
+
+        Note: the background material currently applies to the native-2D
+        BoundaryMode domain (the region outside the stack/cladding); the 3D
+        airbox region remains air.
+
         Args:
             margin_x: Airbox x-margin around the design (um).
                 Defaults to ``0.0`` when omitted.
@@ -209,6 +331,8 @@ def set_airbox(
                 Defaults to ``0.0`` when omitted.
             z_below: Airbox extension below the stack bottom (um).
                 Defaults to ``0.0`` when omitted.
+            material: Background material name for the padded region
+                (default ``"air"``).
         """
         mx = 0.0 if margin_x is None else margin_x
         my = 0.0 if margin_y is None else margin_y
@@ -221,6 +345,8 @@ def set_airbox(
             raise ValueError("margin_y must be >= 0")
         if za < 0 or zb < 0:
             raise ValueError("z_above and z_below must be >= 0")
+        if not material or not isinstance(material, str):
+            raise ValueError("material must be a non-empty string")
 
         # Keep mesh margin controls in sync for domain/port extents.
         mesh_config = getattr(self, "mesh_config", None)
@@ -234,6 +360,7 @@ def set_airbox(
             "margin_y": my,
             "z_above": za,
             "z_below": zb,
+            "material": material,
         }
 
     def _apply_airbox_overrides(
@@ -259,6 +386,46 @@ def _apply_airbox_overrides(
             margin_y=margin_y if margin_y is not None else current.get("margin_y"),
             z_above=z_above if z_above is not None else current.get("z_above"),
             z_below=z_below if z_below is not None else current.get("z_below"),
+            material=str(current.get("material", "air")),
+        )
+
+    # -------------------------------------------------------------------------
+    # Impedance boundaries
+    # -------------------------------------------------------------------------
+
+    def add_impedance_boundary(
+        self,
+        layer_a: str,
+        layer_b: str,
+        *,
+        capacitance: float | None = None,
+        resistance: float | None = None,
+        inductance: float | None = None,
+        name: str | None = None,
+    ) -> None:
+        """Add an Impedance boundary on the interface between two dielectric layers.
+
+        The capacitance, resistance, and inductance values are absolute and
+        are divided by the interface curve length internally to produce the
+        per-unit-length ``Cs``, ``Rs``, ``Ls`` values expected by Palace.
+
+        Args:
+            layer_a: First dielectric layer name.
+            layer_b: Second dielectric layer name.
+            capacitance: Absolute capacitance [F].
+            resistance: Absolute resistance [Ohm].
+            inductance: Absolute inductance [H].
+            name: Optional display name.
+        """
+        self._impedance_boundaries.append(
+            ImpedanceBoundaryConfig(
+                layer_a=layer_a,
+                layer_b=layer_b,
+                capacitance=capacitance,
+                resistance=resistance,
+                inductance=inductance,
+                name=name,
+            )
         )
 
     # -------------------------------------------------------------------------
@@ -643,7 +810,7 @@ def plot_mesh(
         self,
         output: str | Path | None = None,
         show_groups: list[str] | None = None,
-        interactive: bool = True,
+        interactive: bool | None = None,
         style: Literal["wireframe", "solid"] = "wireframe",
         transparent_groups: list[str] | None = None,
     ) -> None:
@@ -652,11 +819,14 @@ def plot_mesh(
         Requires mesh() to be called first.
 
         Args:
-            output: Output PNG path (only used if interactive=False)
+            output: Output PNG path (only used for static rendering).
             show_groups: List of group name patterns to show (None = all).
                 Example: ["metal", "P"] to show metal layers and ports.
-            interactive: If True, open interactive 3D viewer.
-                If False, save static PNG to output path.
+            interactive: If True, force an interactive 3D viewer (a widget on
+                the shared trame server in a notebook, or a blocking window
+                otherwise).  If False, save a static PNG.  If None (default),
+                follow the session flag from ``gsim.viz.set_interactive_mode``
+                — off by default, so plots render statically until enabled.
             style: ``"wireframe"`` (edges only) or ``"solid"`` (coloured
                 surfaces per physical group).
             transparent_groups: Group names rendered at low opacity in
@@ -679,8 +849,8 @@ def plot_mesh(
         if not mesh_path.exists():
             raise ValueError(f"Mesh file not found: {mesh_path}. Call mesh() first.")
 
-        # Default output path if not interactive
-        if output is None and not interactive:
+        # Default output path for the static rendering path.
+        if output is None and interactive is not True:
             output = self._output_dir / "mesh.png"
 
         _plot_mesh(
@@ -959,6 +1129,7 @@ def _generate_mesh_internal(
             airbox_margin_y=airbox_cfg.get("margin_y"),
             airbox_z_above=airbox_cfg.get("z_above"),
             airbox_z_below=airbox_cfg.get("z_below"),
+            airbox_material=airbox_cfg.get("material", "air"),
             fmax=effective_fmax,
             show_gui=mesh_config.show_gui,
             simulation_type=self.simulation_type,
@@ -996,6 +1167,51 @@ def _generate_mesh_internal(
             mesh_stats=mesh_result.mesh_stats,
         )
 
+    def print_mesh_stats(self) -> None:
+        """Print mesh statistics from the last mesh generation.
+
+        Reports node/element counts and estimates solver DOFs based on
+        the solver polynomial order (default 2 for 2D, 1 for 3D).
+        """
+        mr = self._last_mesh_result
+        if mr is None:
+            print("No mesh result. Call mesh() first.")  # noqa: T201
+            return
+
+        stats = mr.mesh_stats or {}
+        groups = mr.groups or {}
+
+        nodes = stats.get("nodes", 0)
+        elements = stats.get("elements", 0)
+        tets = stats.get("tetrahedra", 0)
+
+        bbox = stats.get("bbox", {})
+        if bbox:
+            dx = bbox.get("xmax", 0) - bbox.get("xmin", 0)
+            dy = bbox.get("ymax", 0) - bbox.get("ymin", 0)
+            dz = bbox.get("zmax", 0) - bbox.get("zmin", 0)
+            print(f"  Bounding box: {dx:.3f} x {dy:.3f} x {dz:.3f} um")  # noqa: T201
+
+        print(f"  Nodes:     {nodes:,}")  # noqa: T201
+        print(f"  Elements:  {elements:,}")  # noqa: T201
+        if tets:
+            print(f"  Tetrahedra: {tets:,}")  # noqa: T201
+
+        dom_volumes = groups.get("volumes", {})
+        bdr_conductors = groups.get("conductor_surfaces", {})
+        bdr_interfaces = groups.get("interface_surfaces", {})
+        print(f"  Domain groups:     {len(dom_volumes)}")  # noqa: T201
+        print(f"  Conductor surfaces:{len(bdr_conductors)}")  # noqa: T201
+        print(f"  Interface surfaces:{len(bdr_interfaces)}")  # noqa: T201
+
+        if elements and not tets:
+            p = 2
+            nd_dofs_est = elements * p * (p + 1)
+            h1_dofs_est = elements * (p + 1) * (p + 2) // 2
+            print(f"  Est. ND-space DOFs (order {p}):  ~{nd_dofs_est:,}")  # noqa: T201
+            print(f"  Est. H1-space DOFs (order {p}):  ~{h1_dofs_est:,}")  # noqa: T201
+            print(f"  Est. total DOFs:                  ~{nd_dofs_est + h1_dofs_est:,}")  # noqa: T201
+
     def _get_ports_for_preview(self, stack: LayerStack) -> list:
         """Get ports for preview."""
         from gsim.palace.ports import extract_ports
@@ -1140,6 +1356,7 @@ def preview(
                 airbox_margin_y=airbox_cfg.get("margin_y"),
                 airbox_z_above=airbox_cfg.get("z_above"),
                 airbox_z_below=airbox_cfg.get("z_below"),
+                airbox_material=airbox_cfg.get("material", "air"),
                 fmax=mesh_config.fmax,
                 show_gui=True,
                 simulation_type=self.simulation_type,
@@ -1422,6 +1639,12 @@ def write_config(
         stack = self._resolve_stack()
         electrostatic_config = getattr(self, "electrostatic", None)
         terminals = getattr(self, "terminals", None)
+
+        # Thread impedance boundary configs through hints
+        hints = dict(self._hints)
+        if self._impedance_boundaries:
+            hints["_impedance_boundaries"] = self._impedance_boundaries
+
         config_path = gen_write_config(
             mesh_result=self._last_mesh_result,
             stack=stack,
@@ -1432,7 +1655,7 @@ def write_config(
             numerical_config=self.numerical,
             boundary_mode_config=getattr(self, "boundary_mode", None),
             absorbing_boundary=self.absorbing_boundary,
-            hints=self._hints,
+            hints=hints,
             electrostatic_config=electrostatic_config,
             terminals=terminals or [],
         )
@@ -1613,7 +1836,7 @@ def run_local(
         *,
         palace_sif_path: str | Path | None = None,
         palace_executable: str | Path | None = None,
-        use_apptainer: bool = True,
+        use_apptainer: bool = False,
         num_processes: int | None = None,
         num_threads: int | None = None,
         verbose: bool = True,
@@ -1638,10 +1861,16 @@ def run_local(
             use_apptainer: If True (default), run via Apptainer using SIF file.
                 If False, run Palace executable directly.
                 Ignored when ``palace_executable`` is explicitly provided.
-            num_processes: Number of MPI processes. If None (default),
-                uses all available CPUs.
-            num_threads: Number of OpenMP threads to use for OpenMP builds, default is 1
-                or the value of OMP_NUM_THREADS in the environment
+            num_processes: Number of MPI processes. If None (default), a
+                problem-size-aware default is chosen: 2D mode-analysis runs
+                use a single MPI rank (SuperLU_DIST's 2D processor grid does
+                not scale on small 2D problems and can effectively hang at
+                8-16 ranks), while 3D runs are capped to a few ranks by the
+                estimated unknown count. An explicit value is always respected.
+            num_threads: Number of OpenMP threads to use for OpenMP builds.
+                When running with a single MPI rank and ``num_threads`` is
+                omitted, defaults to the number of physical CPU cores so
+                shared-memory parallelism is used.
             verbose: Print progress messages and stream Palace output in real time
 
         Returns:
@@ -1691,9 +1920,48 @@ def run_local(
         config_path = output_dir / "config.json"
         mesh_path = output_dir / "palace.msh"
 
-        # Default to all available CPUs when caller does not specify -np.
+        # Choose safe parallel defaults. SuperLU_DIST's 2D processor grid does
+        # not scale on small problems (2D mode analysis at 8-16 ranks hangs),
+        # so 2D runs use a single MPI rank + OpenMP threads, and 3D direct
+        # solves are capped by problem size.
+        mesh_stats = {}
+        if self._last_mesh_result is not None:
+            mesh_stats = self._last_mesh_result.mesh_stats or {}
+
         if num_processes is None:
-            num_processes = os.cpu_count() or 1
+            num_processes, num_threads = _recommend_parallel(
+                mesh_stats,
+                self.simulation_type,
+                None,
+                num_threads,
+            )
+            if verbose:
+                logger.info(
+                    "Parallel config: %d MPI rank(s)%s",
+                    num_processes,
+                    f", {num_threads} OpenMP thread(s)" if num_threads else "",
+                )
+        else:
+            # Explicit request: keep it, but warn when it exceeds what the
+            # sparse-direct solver can use efficiently on this problem.
+            rec_processes, _rec_threads = _recommend_parallel(
+                mesh_stats,
+                self.simulation_type,
+                None,
+                None,
+            )
+            if num_processes > rec_processes:
+                logger.warning(
+                    "Requested %d MPI ranks but SuperLU_DIST direct solve "
+                    "does not scale beyond %d rank(s) on this problem size; "
+                    "the factorization may be pathologically slow. Pass "
+                    "num_processes=%d or use OpenMP threads instead.",
+                    num_processes,
+                    rec_processes,
+                    rec_processes,
+                )
+            if num_processes == 1 and num_threads is None:
+                num_threads = _count_physical_cpus()
 
         # Check required files exist
         if not config_path.exists():
@@ -1824,10 +2092,34 @@ def run_local(
                         resolved_exe = bundled
                         lib_dir = resolve_palace_library_dir()
                         if verbose:
+                            from gsim.palace.runtime import (
+                                _palace_cpu_available as _cpu_avail,
+                            )
+
+                            source = (
+                                "palace-toolkit-cpu"
+                                if _cpu_avail()
+                                else "PALACE_BIN / PATH"
+                            )
                             logger.info(
-                                "Using Palace binary from runtime resolver: %s",
+                                "Palace binary: %s  (source: %s)",
                                 bundled,
+                                source,
                             )
+                            try:
+                                import subprocess as _sp
+
+                                ver = _sp.run(  # noqa: S603
+                                    [str(bundled), "--version"],
+                                    capture_output=True,
+                                    text=True,
+                                    timeout=10,
+                                    check=False,
+                                )
+                                if ver.returncode == 0:
+                                    logger.info(ver.stdout.strip())
+                            except Exception:
+                                pass
                     else:
                         # Last resort: "palace" in PATH
                         resolved_exe = "palace"
diff --git a/src/gsim/palace/boundarymode.py b/src/gsim/palace/boundarymode.py
index d1180508..4b9f1b6d 100644
--- a/src/gsim/palace/boundarymode.py
+++ b/src/gsim/palace/boundarymode.py
@@ -63,7 +63,8 @@ class BoundaryModeSim(PalaceSimMixin, BaseModel):
     _stack_kwargs: dict[str, Any] = PrivateAttr(default_factory=dict)
     _pec_blocks: list = PrivateAttr(default_factory=list)
     _hints: dict[str, Any] = PrivateAttr(default_factory=dict)
-    _airbox_config: dict[str, float] = PrivateAttr(default_factory=dict)
+    _impedance_boundaries: list = PrivateAttr(default_factory=list)
+    _airbox_config: dict[str, Any] = PrivateAttr(default_factory=dict)
 
     # Internal state
     _output_dir: Path | None = PrivateAttr(default=None)
diff --git a/src/gsim/palace/driven.py b/src/gsim/palace/driven.py
index 44e45166..39e1fae8 100644
--- a/src/gsim/palace/driven.py
+++ b/src/gsim/palace/driven.py
@@ -90,9 +90,10 @@ class DrivenSim(PalaceSimMixin, BaseModel):
 
     # Stack configuration (stored as kwargs until resolved)
     _stack_kwargs: dict[str, Any] = PrivateAttr(default_factory=dict)
-    _airbox_config: dict[str, float] = PrivateAttr(default_factory=dict)
+    _airbox_config: dict[str, Any] = PrivateAttr(default_factory=dict)
     _pec_blocks: list = PrivateAttr(default_factory=list)
     _hints: dict[str, Any] = PrivateAttr(default_factory=dict)
+    _impedance_boundaries: list = PrivateAttr(default_factory=list)
 
     # Internal state
     _output_dir: Path | None = PrivateAttr(default=None)
diff --git a/src/gsim/palace/eigenmode.py b/src/gsim/palace/eigenmode.py
index 53d1b723..a23c12e2 100644
--- a/src/gsim/palace/eigenmode.py
+++ b/src/gsim/palace/eigenmode.py
@@ -84,9 +84,10 @@ class EigenmodeSim(PalaceSimMixin, BaseModel):
 
     # Stack configuration (stored as kwargs until resolved)
     _stack_kwargs: dict[str, Any] = PrivateAttr(default_factory=dict)
-    _airbox_config: dict[str, float] = PrivateAttr(default_factory=dict)
+    _airbox_config: dict[str, Any] = PrivateAttr(default_factory=dict)
     _pec_blocks: list = PrivateAttr(default_factory=list)
     _hints: dict[str, Any] = PrivateAttr(default_factory=dict)
+    _impedance_boundaries: list = PrivateAttr(default_factory=list)
 
     # Internal state
     _output_dir: Path | None = PrivateAttr(default=None)
diff --git a/src/gsim/palace/electrostatic.py b/src/gsim/palace/electrostatic.py
index ec24ae26..e455ec7f 100644
--- a/src/gsim/palace/electrostatic.py
+++ b/src/gsim/palace/electrostatic.py
@@ -84,9 +84,10 @@ class ElectrostaticSim(PalaceSimMixin, BaseModel):
 
     # Stack configuration (stored as kwargs until resolved)
     _stack_kwargs: dict[str, Any] = PrivateAttr(default_factory=dict)
-    _airbox_config: dict[str, float] = PrivateAttr(default_factory=dict)
+    _airbox_config: dict[str, Any] = PrivateAttr(default_factory=dict)
     _pec_blocks: list = PrivateAttr(default_factory=list)
     _hints: dict[str, Any] = PrivateAttr(default_factory=dict)
+    _impedance_boundaries: list = PrivateAttr(default_factory=list)
 
     # Internal state
     _output_dir: Path | None = PrivateAttr(default=None)
diff --git a/src/gsim/palace/field_viz.py b/src/gsim/palace/field_viz.py
index e69c319e..8a6dc098 100644
--- a/src/gsim/palace/field_viz.py
+++ b/src/gsim/palace/field_viz.py
@@ -3,18 +3,67 @@
 from __future__ import annotations
 
 import logging
+from collections.abc import Sequence
 from dataclasses import dataclass
 from pathlib import Path
 from typing import Any, Literal, cast
 
 import numpy as np
 import pyvista as pv
+from pyvista.plotting._typing import ColormapOptions
 
 from gsim.palace.results import load_fields
 
 logger = logging.getLogger(__name__)
 
 
+def resolve_physical_groups(
+    source: str | Path,
+    group_names: Sequence[str],
+) -> list[int]:
+    """Resolve physical group names to Palace attribute values.
+
+    Reads the mesh file's physical group definitions and returns the
+    numeric attribute values corresponding to the requested group names.
+
+    Args:
+        source: Path to the simulation output directory (containing
+            ``palace.msh``) or directly to the ``.msh`` file.
+        group_names: Physical group names to resolve (e.g.
+            ``["n_rib", "p_rib", "slab90"]``).
+
+    Returns:
+        List of attribute values (integer tags) to use for cell filtering
+        in Palace Paraview output.
+    """
+    import meshio
+
+    path = Path(source)
+    if path.suffix != ".msh":
+        path = path / "palace.msh"
+    if not path.exists():
+        msg = f"Mesh file not found: {path}"
+        raise FileNotFoundError(msg)
+
+    m = meshio.read(str(path))
+    if not hasattr(m, "field_data") or not m.field_data:
+        msg = f"No physical groups found in mesh: {path}"
+        raise ValueError(msg)
+
+    requested = set(group_names)
+    found: list[int] = []
+    missing = set(requested)
+    for name, (tag, _dim) in m.field_data.items():
+        if name in requested:
+            found.append(int(tag))
+            missing.discard(name)
+    if missing:
+        available = sorted(m.field_data.keys())
+        msg = f"Physical group(s) not found: {sorted(missing)}. Available: {available}"
+        raise ValueError(msg)
+    return found
+
+
 Axis = Literal["x", "y", "z"]
 
 
@@ -236,99 +285,160 @@ def plot_fields_2d(
     excitation: int = 1,
     cycle: int | None = None,
     boundary: bool = False,
-    grid_resolution: tuple[int, int] = (360, 240),
-    streamplot_density: float = 1.0,
-    streamplot_linewidth: float = 0.9,
-    streamplot_color: str = "lightskyblue",
-    streamplot_show_arrows: bool = True,
-    streamplot_normalize: bool = False,
-    streamplot_seed_from_field: bool = True,
-    streamplot_seed_frac: float = 0.2,
-    streamplot_seed_stride: int = 2,
-    streamplot_mask_weak: bool = False,
-    streamplot_min_frac: float = 0.08,
-    use_targeted_gap_seeds: bool = True,
-    targeted_seed_offset: float = 8.0,
-    streamplot_minlength: float = 0.1,
-    streamplot_maxlength: float = 2.8,
-    cmap: str = "hot",
-    title: str = "In-plane |E_t|",
-    figsize: tuple[float, float] = (10.0, 5.0),
-    dpi: float = 140.0,
+    physical_groups: Sequence[str] | None = None,
+    cmap: ColormapOptions = "hot",
+    clim: tuple[float, float] | None = None,
+    title: str = "|E|",
+    show_edges: bool = False,
+    opacity: float = 1.0,
     show: bool = True,
-) -> tuple[Any, Any, StreamplotInputs2D]:
-    """Plot 2D in-plane field magnitude and streamlines using Matplotlib.
-
-    This utility centralizes the notebook plotting workflow and returns
-    ``(fig, ax, stream_inputs)`` for custom post-processing.
+    interactive: bool | None = None,
+    screenshot: str | Path | None = None,
+    mode: Literal["auto", "live", "static"] = "auto",
+) -> Any:
+    """Plot 2D field using PyVista, rendering directly on the mesh.
+
+    When *physical_groups* is given, only cells belonging to those mesh
+    physical groups are kept before plotting.  The group names are resolved
+    to attribute values via :func:`resolve_physical_groups`.
+
+    The color scale is clamped to the 98th percentile of the data by
+    default to prevent outlier values (e.g. surface currents on
+    conductors) from washing out the visualization.  Pass *clim* to
+    override.
+
+    Args:
+        source: Simulation output directory, path to ``.pvtu`` / ``.vtu``,
+            or a pre-loaded ``pv.DataSet``.
+        field: Field name to plot (e.g. ``"E_real"``, ``"E_imag"``).
+        normal: Slice normal (``"x"``, ``"y"``, ``"z"``).
+        origin: Slice origin along the normal axis.
+        physical_groups: Optional list of physical group names to
+            restrict the plot to (e.g. ``["n_rib", "p_rib", "slab90"]``).
+        cmap: Colour-map name passed to PyVista.
+        clim: Optional ``(vmin, vmax)`` for the color scale.  If None,
+            ``vmax`` is set to the 98th percentile of the data.
+        title: Plot title.
+        show_edges: Toggle mesh edges on/off.
+        opacity: Opacity of the mesh (0-1).
+        show: If True, display the plot (live view or static image); if
+            False, the plotter is created and returned without rendering.
+        interactive: If ``True``, force an interactive view: in a notebook
+            this renders as a widget on the single shared trame server (so
+            several views can coexist); otherwise it opens a blocking window.
+            ``False`` forces a static PNG.  ``None`` (default) follows the
+            session flag from ``gsim.viz.set_interactive_mode`` — off by
+            default, so plots render statically until it is enabled.
+        screenshot: If given, save a screenshot to this path.
+        mode: Rendering mode: ``"auto"`` (default), ``"live"`` or
+            ``"static"``.  Overrides ``GSIM_VIZ_MODE`` for this call.
+            Interactive views are off by default; enable them globally with
+            ``gsim.viz.set_interactive_mode(True)``.  Close open views with
+            ``gsim.viz.close_interactive_views()``.  The camera always faces
+            the cross-section plane, including for interactive views.
+
+    Returns:
+        The ``pv.Plotter`` instance.
     """
-    import matplotlib.pyplot as plt
+    from gsim.viz import _apply_front_camera, _ensure_pyvista, _show_or_screenshot
 
-    stream_inputs = extract_streamplot_inputs_2d(
+    _ensure_pyvista()
+    import pyvista as pv
+
+    dataset = _source_to_dataset(
         source,
-        field=field,
-        normal=normal,
-        origin=origin,
         excitation=excitation,
         cycle=cycle,
         boundary=boundary,
-        streamplot_density=streamplot_density,
-        streamplot_normalize=streamplot_normalize,
-        streamplot_seed_from_field=streamplot_seed_from_field,
-        streamplot_seed_frac=streamplot_seed_frac,
-        streamplot_seed_stride=streamplot_seed_stride,
-        streamplot_mask_weak=streamplot_mask_weak,
-        streamplot_min_frac=streamplot_min_frac,
-        grid_resolution=grid_resolution,
     )
 
-    x_grid, y_grid = np.meshgrid(stream_inputs.x, stream_inputs.y)
-    fig, ax = plt.subplots(figsize=figsize, dpi=dpi)
-    et = np.asarray(stream_inputs.et_mag, dtype=float)
-    im = ax.pcolormesh(x_grid, y_grid, et, cmap=cmap, shading="gouraud")
-
-    start_points = stream_inputs.start_points
-    if use_targeted_gap_seeds and start_points.shape[0] >= 2:
-        start_points = np.vstack(
-            [
-                start_points + np.array([0.0, targeted_seed_offset]),
-                start_points + np.array([0.0, -targeted_seed_offset]),
-            ]
+    if physical_groups is not None:
+        if not isinstance(source, (str, Path)):
+            msg = "physical_groups requires a file path (not a DataSet or dict)"
+            raise TypeError(msg)
+        source_path = Path(source)
+        output_dir = source_path if source_path.is_dir() else source_path.parent
+        attribute_values = resolve_physical_groups(output_dir, physical_groups)
+
+        if "attribute" not in dataset.cell_data:
+            msg = (
+                "Dataset has no cell_data['attribute'] "
+                "— cannot filter by physical group"
+            )
+            raise ValueError(msg)
+        attrs = np.asarray(dataset.cell_data["attribute"])
+        keep = np.where(np.isin(attrs, np.asarray(attribute_values)))[0]
+        if keep.size == 0:
+            msg = (
+                f"No cells found for physical_groups={physical_groups} "
+                f"(attrs={attribute_values})"
+            )
+            raise ValueError(msg)
+        logger.info(
+            "Selected %d / %d cells for physical_groups=%s",
+            len(keep),
+            dataset.n_cells,
+            physical_groups,
         )
-    start_points = _filter_start_points_in_bounds(
-        start_points,
-        x=stream_inputs.x,
-        y=stream_inputs.y,
+        dataset = dataset.extract_cells(keep)
+
+    # Slice to the cross-section plane.
+    sliced, _used_normal, _axis_idx, _axes = _slice_plane(
+        dataset,
+        normal=normal,
+        origin=origin,
     )
 
-    stream_kwargs: dict[str, Any] = {
-        "x": stream_inputs.x,
-        "y": stream_inputs.y,
-        "u": stream_inputs.u,
-        "v": stream_inputs.v,
-        "color": streamplot_color,
-        "density": streamplot_density,
-        "linewidth": streamplot_linewidth,
-        "arrowsize": 1.0 if streamplot_show_arrows else 1e-6,
-        "arrowstyle": "-|>" if streamplot_show_arrows else "-",
-        "minlength": streamplot_minlength,
-        "maxlength": streamplot_maxlength,
-        "integration_direction": "both",
-    }
-    if start_points.shape[0] >= 2:
-        stream_kwargs["start_points"] = start_points
-
-    ax.streamplot(**stream_kwargs)
-    ax.set_title(title)
-    ax.set_aspect("equal")
-    label_h, label_v = _plane_axis_labels(stream_inputs.normal)
-    ax.set_xlabel(label_h)
-    ax.set_ylabel(label_v)
-    fig.colorbar(im, ax=ax, label="E_t")
-    plt.tight_layout()
+    if field not in sliced.point_data:
+        available = list(sliced.point_data.keys())
+        msg = f"Field '{field}' not found in dataset. Available: {available}"
+        raise ValueError(msg)
+
+    # Determine the 2D scalar to plot (magnitude for vector fields).
+    raw = np.asarray(sliced.point_data[field])
+    if raw.ndim == 2:
+        scalars = np.linalg.norm(raw, axis=1)
+        scalar_name = f"|{field}|"
+        sliced.point_data[scalar_name] = scalars
+    else:
+        scalar_name = field
+
+    # Clamp color scale to 98th percentile (3D-style), unless user overrides.
+    if clim is not None:
+        _clim = clim
+    else:
+        s = np.asarray(sliced.point_data[scalar_name])
+        finite = s[np.isfinite(s)]
+        if finite.size > 0:
+            vmax = float(np.percentile(finite, 98))
+            _clim = (0.0, vmax) if vmax > 0 else None
+        else:
+            _clim = None
+
+    # Camera: face the 2D plane directly (always, not just for zoom).
+    pl = pv.Plotter(window_size=[1200, 900])
+    pl.add_mesh(
+        sliced,
+        scalars=scalar_name,
+        cmap=cmap,
+        clim=_clim,
+        show_edges=show_edges,
+        opacity=opacity,
+        scalar_bar_args={"title": scalar_name, "vertical": True},
+    )
+    pl.add_title(title, font_size=12)
+
+    _apply_front_camera(pl, np.asarray(sliced.points), _axis_idx)
+    if screenshot is not None:
+        pl.screenshot(str(screenshot))
+        pl.close()
+        return pl
+
     if show:
-        plt.show()
-    return fig, ax, stream_inputs
+        _show_or_screenshot(pl, interactive=interactive, mode=mode, reset_camera=False)
+    else:
+        pl.close()
+    return pl
 
 
 def extract_streamplot_inputs_2d(
diff --git a/src/gsim/palace/mesh/config_generator.py b/src/gsim/palace/mesh/config_generator.py
index 28df3a04..bb81add0 100644
--- a/src/gsim/palace/mesh/config_generator.py
+++ b/src/gsim/palace/mesh/config_generator.py
@@ -6,6 +6,7 @@
 from __future__ import annotations
 
 import json
+import logging
 from pathlib import Path
 from typing import TYPE_CHECKING, Any, Literal
 
@@ -13,6 +14,8 @@
 
 from gsim.palace.ports.config import PortType
 
+logger = logging.getLogger(__name__)
+
 if TYPE_CHECKING:
     from gsim.common.stack import LayerStack
     from gsim.palace.models import (
@@ -26,6 +29,94 @@
     from gsim.palace.ports.config import PalacePort
 
 
+def _resolve_impedance_boundaries(
+    hints: dict[str, Any] | None,
+    groups: dict,
+) -> list[dict[str, object]]:
+    """Resolve impedance boundary configs from hints into Palace format entries.
+
+    For interface-based entries (layer_a + layer_b), looks up the interface
+    physical group and divides absolute values by the stored curve length.
+    For attribute-based entries, uses the values as-is.
+
+    Returns:
+        List of dicts suitable for the Palace ``Impedance`` boundary section.
+    """
+    from gsim.palace.models.ports import ImpedanceBoundaryConfig
+
+    raw = (hints or {}).get("_impedance_boundaries")
+    if not raw:
+        return []
+
+    entries: list[dict[str, object]] = []
+    for ib in raw:
+        if not isinstance(ib, ImpedanceBoundaryConfig):
+            continue
+
+        if ib.attributes is not None:
+            # Attribute-based: use values directly (already per-unit-length).
+            entry: dict[str, object] = {
+                "Attributes": sorted(ib.attributes),
+            }
+            if ib.resistance is not None:
+                entry["Rs"] = ib.resistance
+            if ib.inductance is not None:
+                entry["Ls"] = ib.inductance
+            if ib.capacitance is not None:
+                entry["Cs"] = ib.capacitance
+            entries.append(entry)
+            continue
+
+        # Interface-based: look up the interface physical group.
+        candidates = [
+            f"interface_{ib.layer_a}_{ib.layer_b}",
+            f"interface_{ib.layer_b}_{ib.layer_a}",
+        ]
+        group_info = None
+        for name in candidates:
+            info = groups.get("interface_surfaces", {}).get(name)
+            if info is not None:
+                group_info = info
+                break
+
+        if group_info is None:
+            logger.warning(
+                "Impedance boundary interface '%s' / '%s' not found in mesh. "
+                "Available interfaces: %s",
+                ib.layer_a,
+                ib.layer_b,
+                ", ".join(sorted(groups.get("interface_surfaces", {}).keys())),
+            )
+            continue
+
+        entry: dict[str, object] = {
+            "Attributes": [group_info["phys_group"]],
+        }
+
+        # Convert absolute values to per-unit-length using the stored length.
+        length_um = group_info.get("length_um", 0.0)
+        if length_um <= 0.0:
+            logger.warning(
+                "Interface '%s' / '%s' has zero or unknown length; "
+                "using absolute values directly.",
+                ib.layer_a,
+                ib.layer_b,
+            )
+            length_um = 1.0  # fallback: treat as 1 um
+
+        length_m = length_um * 1e-6
+        if ib.resistance is not None:
+            entry["Rs"] = ib.resistance / length_m
+        if ib.inductance is not None:
+            entry["Ls"] = ib.inductance / length_m
+        if ib.capacitance is not None:
+            entry["Cs"] = ib.capacitance / length_m
+
+        entries.append(entry)
+
+    return entries
+
+
 def generate_palace_config(
     groups: dict,
     ports: list[PalacePort],
@@ -179,7 +270,11 @@ def generate_palace_config(
     }
 
     # Build domains section
-    # Evaluate dispersion models at the center frequency of the sweep band
+    # Evaluate dispersion models at the problem's target frequency. Driven
+    # simulations use the sweep center frequency; boundary mode (2D waveguide
+    # cross-section) uses its single operating frequency so optical modes are
+    # computed with the true frequency-resolved permittivity (e.g. Sellmeier
+    # silicon at 1550 nm) rather than the RF constant values.
     stack_materials = stack.materials
     if driven_config is not None:
         from gsim.palace.materials import resolve_palace_materials_at_frequency
@@ -187,6 +282,12 @@ def generate_palace_config(
         stack_materials = resolve_palace_materials_at_frequency(
             stack.materials, driven_config.center_frequency
         )
+    elif boundary_mode_config is not None:
+        from gsim.palace.materials import resolve_palace_materials_at_frequency
+
+        stack_materials = resolve_palace_materials_at_frequency(
+            stack.materials, boundary_mode_config.freq
+        )
 
     # Support material keys with different capitalization conventions
     # between stack layers and material dictionaries.
@@ -238,6 +339,15 @@ def _lookup_material(name: str) -> dict[str, object]:
             else:
                 mat_entry["LossTan"] = 0.0
 
+            # Finite-conductivity shaped dielectrics (e.g. doped silicon)
+            # need a Conductivity entry so Palace treats them as lossy
+            # semiconductors rather than ideal dielectrics.
+            sigma = mat_props.get("conductivity", 0.0)
+            if (isinstance(sigma, (int, float)) and sigma > 0) or isinstance(
+                sigma, list
+            ):
+                mat_entry["Conductivity"] = sigma
+
             if "permeability" in mat_props:
                 mat_entry["Permeability"] = mat_props["permeability"]
 
@@ -293,7 +403,7 @@ def _lookup_material(name: str) -> dict[str, object]:
     pec_attrs: list[int] = [
         info["phys_group"] for info in groups.get("pec_surfaces", {}).values()
     ]
-    boundaries: dict[str, object]
+    boundaries: dict[str, Any]
 
     is_electrostatic = simulation_type in ("electrostatic", "electrostatics")
 
@@ -368,7 +478,7 @@ def _via_touches(via_name: str, conductor_layer_name: str) -> bool:
                     ground_attrs.extend(via_pgs)
                     break
 
-        boundaries: dict[str, object] = {
+        boundaries: dict[str, Any] = {
             "Terminal": terminal_entries,
         }
         if ground_attrs:
@@ -499,7 +609,7 @@ def _via_touches(via_name: str, conductor_layer_name: str) -> bool:
             synthetic_idx += 1
         lumped_ports.extend(passive_reactive_ports)
 
-        boundaries: dict[str, object] = {
+        boundaries: dict[str, Any] = {
             "Conductivity": conductors,
             "LumpedPort": lumped_ports,
             "WavePort": wave_ports,
@@ -565,11 +675,17 @@ def _via_touches(via_name: str, conductor_layer_name: str) -> bool:
             ],
         }
 
+    # Process impedance boundaries from hints (interface-based or attribute-based)
+    impedance_entries = _resolve_impedance_boundaries(hints, groups)
+    if impedance_entries:
+        boundaries.setdefault("Impedance", []).extend(impedance_entries)
+
     config["Boundaries"] = boundaries
 
-    # Merge any extra hints into the config
+    # Merge any extra hints into the config (strip internal keys first)
     if hints:
-        config.update(hints)
+        clean_hints = {k: v for k, v in hints.items() if not k.startswith("_")}
+        config.update(clean_hints)
 
     # Write config file
     config_path = output_path / "config.json"
diff --git a/src/gsim/palace/mesh/generator.py b/src/gsim/palace/mesh/generator.py
index 11c15903..950310e2 100644
--- a/src/gsim/palace/mesh/generator.py
+++ b/src/gsim/palace/mesh/generator.py
@@ -249,6 +249,25 @@ def _curve_on_native_2d_domain_wall(
     return on_hmin or on_hmax or on_vmin or on_vmax
 
 
+def _ensure_background_material(stack, material: str) -> None:
+    """Ensure *material* has an entry in ``stack.materials``.
+
+    The native-2D background volume is grouped under ``airbox_material``. If
+    that name is not already in the stack's materials dict, populate it from
+    the built-in database so the config generator can resolve its permittivity
+    (falling back to eps=1 for unknown names).
+    """
+    from gsim.common.stack.materials import get_material_properties
+
+    if material in stack.materials:
+        return
+    props = get_material_properties(material)
+    if props is not None:
+        stack.materials[material] = props.to_dict()
+    else:
+        stack.materials[material] = {"permittivity": 1.0, "loss_tangent": 0.0}
+
+
 def _generate_native_boundarymode_groups(
     *,
     kernel,
@@ -263,6 +282,7 @@ def _generate_native_boundarymode_groups(
     airbox_margin_y: float | None,
     airbox_z_above: float | None,
     airbox_z_below: float | None,
+    airbox_material: str = "air",
 ) -> dict:
     """Build a native 2D gmsh model and groups for BoundaryMode."""
     if cross_section.axis not in {"x", "y"}:
@@ -364,6 +384,7 @@ def _generate_native_boundarymode_groups(
         "conductor_surfaces": {},
         "pec_surfaces": {},
         "port_surfaces": {},
+        "interface_surfaces": {},
         "boundary_surfaces": {},
         "refinement_lines": {},
     }
@@ -384,6 +405,85 @@ def _generate_native_boundarymode_groups(
         if layer is not None and layer.layer_type in {"conductor", "via"}:
             metal_piece_tags.update(pieces)
 
+    # Priority-based deduplication for overlapping dielectric layers.
+    #
+    # The gmsh fragment assigns each piece to ALL parent layers that
+    # contain it.  When a patterned layer (e.g. p_rib) is fully inside a
+    # larger patterned layer (e.g. core or slab90), both claim the same
+    # piece.  We resolve this with a priority order:
+    #
+    #   1. Patterned dielectrics with a real GDS layer (doping, rib, slab)
+    #      take priority over background dielectric regions (sio2, passive,
+    #      air) that share the same z-range.
+    #   2. Among overlapping patterned dielectrics, the one with the
+    #      *smaller* total area wins (the doping region carves out of the
+    #      larger silicon region it is embedded in).
+    #
+    # This mirrors the 3D boolean pipeline's mesh_order convention where
+    # smaller / higher-detail volumes carve out of larger background volumes.
+
+    def _is_background_dielectric(layer_name: str) -> bool:
+        """Background dielectric: no real GDS layer (e.g. sio2, passive, air)."""
+        layer = stack.layers.get(layer_name)
+        return layer is None or layer.gds_layer == (999, 0)
+
+    def _is_patterned_dielectric(layer_name: str) -> bool:
+        """Patterned dielectric: has a real GDS layer and is dielectric type."""
+        layer = stack.layers.get(layer_name)
+        return (
+            layer is not None
+            and layer.layer_type == "dielectric"
+            and layer.gds_layer != (999, 0)
+        )
+
+    # Step 1: strip patterned-dielectric pieces from background regions.
+    patterned_piece_tags: set[int] = set()
+    for layer_name, pieces in layer_surfaces.items():
+        if _is_patterned_dielectric(layer_name):
+            patterned_piece_tags.update(pieces)
+
+    if patterned_piece_tags:
+        for layer_name, pieces in list(layer_surfaces.items()):
+            if _is_background_dielectric(layer_name):
+                filtered = pieces - patterned_piece_tags
+                if filtered:
+                    layer_surfaces[layer_name] = filtered
+                else:
+                    layer_surfaces.pop(layer_name, None)
+
+    # Step 2: among patterned dielectrics, resolve overlaps by area.
+    # Compute the bounding-box area of each patterned layer's pieces.
+    patterned_names = [n for n in layer_surfaces if _is_patterned_dielectric(n)]
+
+    def _layer_area(layer_name: str) -> float:
+        """Approximate area of a layer's 2D pieces via bounding boxes."""
+        total = 0.0
+        for stag in layer_surfaces.get(layer_name, set()):
+            try:
+                xmin, ymin, _zmin, xmax, ymax, _zmax = gmsh.model.getBoundingBox(
+                    2, stag
+                )
+                total += (xmax - xmin) * (ymax - ymin)
+            except Exception:
+                pass
+        return total
+
+    # Sort patterned dielectrics by area (smallest first = highest priority).
+    patterned_by_area = sorted(patterned_names, key=_layer_area)
+
+    # For each patterned layer (smallest first), claim its pieces and
+    # remove them from all larger patterned layers.
+    claimed_pieces: set[int] = set()
+    for layer_name in patterned_by_area:
+        pieces = layer_surfaces.get(layer_name, set())
+        # Remove pieces already claimed by smaller (higher-priority) layers.
+        unique = pieces - claimed_pieces
+        if unique:
+            layer_surfaces[layer_name] = unique
+            claimed_pieces.update(unique)
+        else:
+            layer_surfaces.pop(layer_name, None)
+
     if metal_piece_tags:
         for layer_name, pieces in list(layer_surfaces.items()):
             layer = stack.layers.get(layer_name)
@@ -420,33 +520,56 @@ def _is_conductive(value: float | list[float] | None) -> bool:
 
     assigned: set[int] = set()
 
+    # First pass: assign volume physical groups to dielectrics.
+    dielectrics: dict[str, list[int]] = {}
+    metals: dict[str, list[int]] = {}
     for layer_name, surface_tags in sorted(layer_surfaces.items()):
         sorted_tags = sorted(surface_tags)
         layer = stack.layers.get(layer_name)
         is_metal_like = layer is not None and layer.layer_type in {"conductor", "via"}
-
-        # Always consume the conductor interior from air assignment, but do
-        # not export it as a 2D domain material.
         assigned.update(sorted_tags)
-
-        if not is_metal_like:
-            pg = gmsh.model.addPhysicalGroup(2, sorted_tags)
-            gmsh.model.setPhysicalName(2, pg, layer_name)
-
-            entry: dict[str, object] = {
-                "phys_group": pg,
-                "tags": sorted_tags,
-            }
-            # Only layer-backed dielectric polygons are shaped dielectrics.
-            # Background dielectric slabs (e.g. sio2/sin material regions)
-            # should be treated as regular material domains.
-            if layer is not None and layer.layer_type == "dielectric":
-                entry["is_shaped_dielectric"] = True
-            if layer is not None and layer.layer_type == "via":
-                entry["is_via"] = True
-            groups["volumes"][layer_name] = entry
-            continue
-
+        if is_metal_like:
+            metals[layer_name] = sorted_tags
+        else:
+            dielectrics[layer_name] = sorted_tags
+
+    # The 2D domain region not claimed by any dielectric/layer rectangle is the
+    # background medium. By default it is named "air" (eps=1); ``airbox_material``
+    # retunes it to a real cladding material (e.g. "sio2") for uniform-dielectric
+    # optical cross-sections with no air. Merged into the dielectric groups so a
+    # background name matching an existing region (e.g. the oxide "sio2") becomes
+    # one contiguous physical group.
+    bg_tags = sorted(outer_parts - assigned)
+    if bg_tags:
+        _ensure_background_material(stack, airbox_material)
+        dielectrics.setdefault(airbox_material, []).extend(bg_tags)
+        assigned.update(bg_tags)
+
+    for layer_name, sorted_tags in dielectrics.items():
+        layer = stack.layers.get(layer_name)
+        pg = gmsh.model.addPhysicalGroup(2, sorted_tags)
+        gmsh.model.setPhysicalName(2, pg, layer_name)
+        entry: dict[str, object] = {
+            "phys_group": pg,
+            "tags": sorted_tags,
+        }
+        if layer is not None and layer.layer_type == "dielectric":
+            entry["is_shaped_dielectric"] = True
+        if layer is not None and layer.layer_type == "via":
+            entry["is_via"] = True
+        groups["volumes"][layer_name] = entry
+
+    # Build the set of all surface tags that have a volume physical group
+    # (all dielectrics are now assigned).
+    vol_pg_surfaces: set[int] = set()
+    for pg_dim, pg_tag in gmsh.model.getPhysicalGroups():
+        if pg_dim == 2:
+            ents = gmsh.model.getEntitiesForPhysicalGroup(2, pg_tag)
+            vol_pg_surfaces.update(int(e) for e in ents)
+
+    # Second pass: process conductor/via boundary curves (all dielectrics now
+    # have PGs, so the adjacency filter correctly preserves shared edges).
+    for layer_name, sorted_tags in metals.items():
         pec_curves: set[int] = set()
         for stag in sorted_tags:
             try:
@@ -463,7 +586,38 @@ def _is_conductive(value: float | list[float] | None) -> bool:
                     pec_curves.add(ctag)
 
         if pec_curves:
-            curve_tags = sorted(pec_curves)
+            # Some curves may be internal to the conductor pieces (shared
+            # between two conductor surface fragments).  These curves have no
+            # adjacent volume element in the mesh (conductor surfaces are not
+            # written as volume physical groups), so they would cause a
+            # segfault in MFEM's GetBdrElementFace.  Filter them out by
+            # checking gmsh adjacencies: keep a curve only if at least one
+            # adjacent surface actually has a volume physical group.
+            filtered_curves: set[int] = set()
+            n_internal = 0
+            for ctag in pec_curves:
+                try:
+                    adj = gmsh.model.getAdjacencies(1, int(ctag))
+                except Exception:
+                    filtered_curves.add(ctag)
+                    continue
+                adj_surfaces = set(adj[1]) if len(adj) > 1 else set()
+                if not adj_surfaces:
+                    filtered_curves.add(ctag)
+                    continue
+                if adj_surfaces & vol_pg_surfaces:
+                    filtered_curves.add(ctag)
+                else:
+                    n_internal += 1
+            if n_internal > 0:
+                logger.info(
+                    "Filtered %d internal conductor curves for '%s' (%d remaining)",
+                    n_internal,
+                    layer_name,
+                    len(filtered_curves),
+                )
+
+            curve_tags = sorted(filtered_curves)
             sigma = _material_conductivity(layer_name)
             if _is_conductive(sigma):
                 cond_pg = gmsh.model.addPhysicalGroup(1, curve_tags)
@@ -480,11 +634,8 @@ def _is_conductive(value: float | list[float] | None) -> bool:
                     "tags": curve_tags,
                 }
 
-    air_tags = sorted(outer_parts - assigned)
-    if air_tags:
-        air_pg = gmsh.model.addPhysicalGroup(2, air_tags)
-        gmsh.model.setPhysicalName(2, air_pg, "air")
-        groups["volumes"]["air"] = {"phys_group": air_pg, "tags": air_tags}
+    # The 2D background medium (unclaimed domain) is merged into the dielectric
+    # groups above, so nothing to add here.
 
     refinement_curves: set[int] = set()
     for info in groups["conductor_surfaces"].values():
@@ -514,6 +665,56 @@ def _is_conductive(value: float | list[float] | None) -> bool:
             "tags": sorted(refinement_curves)
         }
 
+    # --- Dielectric-dielectric interface curves -------------------------------
+    # Build per-volume boundary curves, then find shared curves between pairs
+    # of dielectric volumes. Each shared curve is assigned a physical group
+    # named "interface_<layer_A>_<layer_B>" and stored under
+    # groups["interface_surfaces"].
+    vol_boundary_curves: dict[str, set[int]] = {}
+    for layer_name, vol_info in groups["volumes"].items():
+        curves: set[int] = set()
+        for stag in vol_info.get("tags", []):
+            try:
+                bounds = gmsh.model.getBoundary(
+                    [(2, int(stag))],
+                    combined=False,
+                    oriented=False,
+                    recursive=False,
+                )
+            except Exception:
+                continue
+            for dim, ctag in bounds:
+                if dim == 1:
+                    curves.add(int(ctag))
+        if curves:
+            vol_boundary_curves[layer_name] = curves
+
+    vol_names = list(vol_boundary_curves.keys())
+    for i, l1 in enumerate(vol_names):
+        for l2 in vol_names[i + 1 :]:
+            shared = vol_boundary_curves[l1] & vol_boundary_curves[l2]
+            if shared:
+                name = f"interface_{l1}_{l2}"
+                pg = gmsh.model.addPhysicalGroup(1, sorted(shared))
+                gmsh.model.setPhysicalName(1, pg, name)
+
+                # Compute approximate total curve length from bounding boxes
+                total_length = 0.0
+                for ctag in shared:
+                    try:
+                        bb = gmsh.model.getBoundingBox(1, int(ctag))
+                        dx = bb[3] - bb[0]
+                        dy = bb[4] - bb[1]
+                        total_length += math.sqrt(dx * dx + dy * dy)
+                    except Exception:
+                        pass
+
+                groups.setdefault("interface_surfaces", {})[name] = {
+                    "phys_group": pg,
+                    "tags": sorted(shared),
+                    "length_um": total_length,
+                }
+
     outer_curves: set[int] = set()
     for stag in outer_parts:
         try:
@@ -797,6 +998,7 @@ def generate_mesh(
     airbox_margin_y: float | None = None,
     airbox_z_above: float | None = None,
     airbox_z_below: float | None = None,
+    airbox_material: str = "air",
     fmax: float = 100e9,
     show_gui: bool = False,
     simulation_type: str = "driven",
@@ -839,6 +1041,9 @@ def generate_mesh(
         airbox_margin_y: Extra y-margin for explicit airbox (um)
         airbox_z_above: Extra +z margin for explicit airbox (um)
         airbox_z_below: Extra -z margin for explicit airbox (um)
+        airbox_material: Material name for the native-2D BoundaryMode background
+            region outside the stack/cladding (default ``"air"``). Pass e.g.
+            ``"sio2"`` for a uniform-dielectric cladding with no air.
         fmax: Max frequency for config (Hz)
         show_gui: Show gmsh GUI during meshing
         simulation_type: Type of simulation (driven, eigenmode or electrostatics)
@@ -921,6 +1126,7 @@ def generate_mesh(
                 airbox_margin_y=airbox_margin_y,
                 airbox_z_above=airbox_z_above,
                 airbox_z_below=airbox_z_below,
+                airbox_material=airbox_material,
             )
 
             refinement_lines = sorted(
diff --git a/src/gsim/palace/models/__init__.py b/src/gsim/palace/models/__init__.py
index c0905072..2e44390c 100644
--- a/src/gsim/palace/models/__init__.py
+++ b/src/gsim/palace/models/__init__.py
@@ -22,6 +22,7 @@
 from gsim.palace.models.pec import PECBlockConfig
 from gsim.palace.models.ports import (
     CPWPortConfig,
+    ImpedanceBoundaryConfig,
     PortConfig,
     TerminalConfig,
     WavePortConfig,
@@ -45,6 +46,7 @@
     "EigenmodeConfig",
     "ElectrostaticConfig",
     "GeometryConfig",
+    "ImpedanceBoundaryConfig",
     "MagnetostaticConfig",
     "MaterialConfig",
     "MeshConfig",
diff --git a/src/gsim/palace/models/ports.py b/src/gsim/palace/models/ports.py
index e66c1c3e..a066369b 100644
--- a/src/gsim/palace/models/ports.py
+++ b/src/gsim/palace/models/ports.py
@@ -133,6 +133,56 @@ class TerminalConfig(BaseModel):
     layer: str
 
 
+class ImpedanceBoundaryConfig(BaseModel):
+    """Configuration for an Impedance boundary on a dielectric-dielectric interface.
+
+    Specifies a surface impedance boundary condition (Rs, Ls, Cs) applied to
+    the shared boundary curve between two dielectric layers.  Capacitance,
+    resistance, and inductance values are given as *absolute* quantities and
+    are divided by the interface curve length internally to obtain the
+    per-unit-length values (Rs, Ls, Cs) expected by Palace.
+
+    Alternatively, ``attributes`` can be specified directly (with Rs/Ls/Cs
+    already in per-unit-length form) for cases where the user already knows
+    the Palace boundary attribute numbers.
+
+    Attributes:
+        layer_a: Name of the first dielectric layer.
+        layer_b: Name of the second dielectric layer.
+        capacitance: Absolute capacitance [F] (divided by curve length).
+        resistance: Absolute resistance [Ohm] (divided by curve length).
+        inductance: Absolute inductance [H] (divided by curve length).
+        attributes: Direct Palace boundary attribute list (bypasses layer lookup).
+            When set, Rs/Ls/Cs must be in per-unit-length values.
+        name: Optional display name.
+    """
+
+    model_config = ConfigDict(validate_assignment=True)
+
+    layer_a: str | None = None
+    layer_b: str | None = None
+    capacitance: float | None = Field(default=None, ge=0, description="Capacitance [F]")
+    resistance: float | None = Field(default=None, ge=0, description="Resistance [Ohm]")
+    inductance: float | None = Field(default=None, ge=0, description="Inductance [H]")
+    attributes: list[int] | None = None
+    name: str | None = None
+
+    @model_validator(mode="after")
+    def _validate_target(self) -> Self:
+        """Validate that exactly one of (layer_a+layer_b) or attributes is set."""
+        if (self.layer_a is None or self.layer_b is None) and self.attributes is None:
+            raise ValueError("Either layer_a+layer_b or attributes must be provided")
+        if (
+            self.layer_a is not None or self.layer_b is not None
+        ) and self.attributes is not None:
+            raise ValueError("Cannot specify both layer_a/layer_b and attributes")
+        if self.layer_a is not None and self.layer_b is None:
+            raise ValueError("Both layer_a and layer_b must be provided together")
+        if self.layer_a is None and self.layer_b is not None:
+            raise ValueError("Both layer_a and layer_b must be provided together")
+        return self
+
+
 class WavePortConfig(BaseModel):
     """Configuration for a wave port (domain boundary with mode solving).
 
@@ -171,6 +221,7 @@ class WavePortConfig(BaseModel):
 
 __all__ = [
     "CPWPortConfig",
+    "ImpedanceBoundaryConfig",
     "PortConfig",
     "TerminalConfig",
     "WavePortConfig",
diff --git a/src/gsim/palace/plane_section.py b/src/gsim/palace/plane_section.py
new file mode 100644
index 00000000..1c49ae97
--- /dev/null
+++ b/src/gsim/palace/plane_section.py
@@ -0,0 +1,162 @@
+"""2D cross-section ('plane section') visualisation.
+
+Given a list of axis-aligned rectangles / polygons produced by
+``gsim.common.cross_section.extract_plane_section`` (e.g. an ``x=0`` cut
+through a component), this module draws a matplotlib 2D cross-section where
+every region is coloured by its layer / physical-group name.
+
+This is the reusable, post-processing version of the inline plot that used to
+live in ``nbs/palace_2d_twmzm.ipynb``.  It is solver-agnostic with respect to
+the *section* data (only the small dataclass types from
+``gsim.common.cross_section`` are required), so it can be used to visualise
+the physical groups of any Palace cross-section.
+
+Supported inputs:
+    - ``Rect2D`` (XZ cut at fixed Y; horizontal axis = x, vertical = z)
+    - ``RectYZ2D`` (YZ cut at fixed X; horizontal axis = y, vertical = z)
+    - ``PolygonXY2D`` (XY cut at fixed Z; polygons in the x-y plane)
+"""
+
+from __future__ import annotations
+
+from typing import Any, Literal
+
+import matplotlib.pyplot as plt
+from matplotlib.axes import Axes
+from matplotlib.patches import Polygon, Rectangle
+
+from gsim.common.cross_section import PolygonXY2D, Rect2D, RectYZ2D
+
+__all__ = ["plot_plane_section"]
+
+_LINE_COLOR = "k"
+_LINE_WIDTH = 0.5
+
+
+def _rect_props(
+    rect: Rect2D | RectYZ2D,
+) -> tuple[tuple[float, float], float, float, tuple[str, str]]:
+    """Return ``((h0, h1), v0, v1, (h_label, v_label))`` for a rectangle."""
+    if isinstance(rect, RectYZ2D):
+        return (rect.y0, rect.y1), rect.zmin, rect.zmax, ("y (um)", "z (um)")
+    return (rect.x0, rect.x1), rect.zmin, rect.zmax, ("x (um)", "z (um)")
+
+
+def _color_map(names: list[str], colors: dict[str, Any] | None) -> dict[str, Any]:
+    """Merge user colours with deterministic ``tab10`` fallbacks."""
+    if colors is None:
+        colors = {}
+    cmap = plt.colormaps.get_cmap("tab10")
+    for i, name in enumerate(dict.fromkeys(names)):
+        colors.setdefault(name, cmap(i % 10))
+    return colors
+
+
+def plot_plane_section(
+    section: list[Any],
+    *,
+    colors: dict[str, Any] | None = None,
+    h_range: tuple[float, float] | None = None,
+    v_range: tuple[float, float] | None = None,
+    title: str | None = None,
+    figsize: tuple[float, float] = (10, 4),
+    aspect: Literal["auto", "equal"] | float = "equal",
+    legend: bool = True,
+    ax: Axes | None = None,
+) -> Axes:
+    """Plot a 2D cross-section coloured by layer / physical-group name.
+
+    Args:
+        section: Regions from ``extract_plane_section`` (``Rect2D``,
+            ``RectYZ2D`` or ``PolygonXY2D``).  A single mixed type is
+            expected per call.
+        colors: Optional ``{layer_name: colour}`` override.  When omitted,
+            colours are drawn deterministically from the ``tab10`` colormap.
+        h_range: ``(h_min, h_max)`` limits for the horizontal axis.  Auto
+            from the section when ``None``.
+        v_range: ``(v_min, v_max)`` limits for the vertical axis.  Auto
+            from the section when ``None``.
+        title: Optional plot title.
+        figsize: Figure size (ignored if *ax* is supplied).
+        aspect: Matplotlib aspect ratio for the axes (e.g. ``"equal"``).
+        legend: Whether to show the per-group legend.
+        ax: Optional existing axes to draw on.  If ``None`` a new figure is
+            created and shown.
+
+    Returns:
+        The ``plt.Axes`` the section was drawn on.
+    """
+    if ax is None:
+        _, ax = plt.subplots(figsize=figsize)
+
+    names = [getattr(r, "layer_name", str(r)) for r in section]
+    color_map = _color_map(names, colors)
+
+    h_lims: list[float] = []
+    v_lims: list[float] = []
+    h_label: str | None = None
+    v_label: str | None = None
+
+    for r in section:
+        name = getattr(r, "layer_name", str(r))
+        color = color_map.get(name, "#dddddd")
+
+        if isinstance(r, (Rect2D, RectYZ2D)):
+            (h0, h1), v0, v1, (hl, vl) = _rect_props(r)
+            h_label = hl
+            v_label = vl
+            h_lims += [h0, h1]
+            v_lims += [v0, v1]
+            ax.add_patch(
+                Rectangle(
+                    (h0, v0),
+                    h1 - h0,
+                    v1 - v0,
+                    facecolor=color,
+                    edgecolor=_LINE_COLOR,
+                    linewidth=_LINE_WIDTH,
+                    alpha=0.8,
+                    label=name,
+                )
+            )
+        elif isinstance(r, PolygonXY2D):
+            h_label = "x (um)"
+            v_label = "y (um)"
+            h_lims += [p[0] for p in r.exterior]
+            v_lims += [p[1] for p in r.exterior]
+            ax.add_patch(
+                Polygon(
+                    r.exterior,
+                    facecolor=color,
+                    edgecolor=_LINE_COLOR,
+                    linewidth=_LINE_WIDTH,
+                    alpha=0.8,
+                    label=name,
+                )
+            )
+        else:
+            msg = f"Unsupported section element: {type(r)!r}"
+            raise TypeError(msg)
+
+    if h_range is not None:
+        ax.set_xlim(*h_range)
+    elif h_lims:
+        ax.set_xlim(min(h_lims), max(h_lims))
+    if v_range is not None:
+        ax.set_ylim(*v_range)
+    elif v_lims:
+        ax.set_ylim(min(v_lims), max(v_lims))
+
+    if h_label is not None:
+        ax.set_xlabel(h_label)
+    if v_label is not None:
+        ax.set_ylabel(v_label)
+    ax.set_aspect(aspect)
+    ax.set_title(title or "Cross-section physical groups")
+
+    if legend:
+        handles, labels = ax.get_legend_handles_labels()
+        by_label = dict(zip(labels, handles, strict=True))
+        ax.legend(by_label.values(), by_label.keys(), loc="upper right", fontsize=8)
+
+    return ax
diff --git a/src/gsim/palace/runtime.py b/src/gsim/palace/runtime.py
index ddcf1ca3..c3f51ef4 100644
--- a/src/gsim/palace/runtime.py
+++ b/src/gsim/palace/runtime.py
@@ -19,6 +19,7 @@
 import logging
 import os
 import shutil
+import subprocess
 from pathlib import Path
 
 logger = logging.getLogger(__name__)
@@ -116,18 +117,22 @@ def resolve_palace_library_dir() -> Path | None:
 
 
 def _binary_is_runnable(binary: Path, timeout: float = 15.0) -> bool:
-    """Quick smoke test — run ``<binary> --version``."""
-    import subprocess
-
+    """Smoke test: file exists, is executable, and responds to --version or --help."""
     bin_str = str(binary)
-    try:
-        result = subprocess.run(  # noqa: S603
-            [bin_str, "--version"],
-            capture_output=True,
-            text=True,
-            timeout=timeout,
-            check=False,
-        )
-    except Exception:
+    if not binary.is_file() or not os.access(bin_str, os.X_OK):
         return False
-    return result.returncode == 0
+
+    for flag in ("--version", "--help"):
+        try:
+            result = subprocess.run(  # noqa: S603
+                [bin_str, flag],
+                capture_output=True,
+                text=True,
+                timeout=timeout,
+                check=False,
+            )
+            if result.returncode == 0:
+                return True
+        except Exception:
+            continue
+    return True  # fallback: just being executable is enough
diff --git a/src/gsim/viz.py b/src/gsim/viz.py
index eb6dd1fe..c3641b52 100644
--- a/src/gsim/viz.py
+++ b/src/gsim/viz.py
@@ -5,19 +5,144 @@
 
 from __future__ import annotations
 
-__all__ = ["plot_cross_section", "plot_mesh", "plot_topview", "sample_topview_field"]
-
+__all__ = [
+    "close_interactive_view",
+    "close_interactive_views",
+    "interactive_mode",
+    "interactive_views",
+    "plot_cross_section",
+    "plot_mesh",
+    "plot_topview",
+    "sample_topview_field",
+    "set_interactive_mode",
+    "set_trame_backend",
+]
+
+import contextlib
 import hashlib
 import logging
+import os
 from pathlib import Path
 from typing import Any, Literal, cast
 
 import meshio
 import numpy as np
-import pyvista as pv
 
 logger = logging.getLogger(__name__)
 
+#: Rendering modes for ``plot_mesh`` / ``plot_fields_2d``.
+RenderMode = Literal["auto", "live", "static"]
+
+#: Global rendering mode, overridable per call.  ``auto`` keeps the current
+#: live PyVista view interactive and renders any additional views in the same
+#: process as static inline images (avoids concurrent live trame servers).
+_VIZ_MODE = os.environ.get("GSIM_VIZ_MODE", "auto").strip().lower() or "auto"
+
+#: Trame backend used for notebook live views.  ``"trame"`` uses server-side
+#: rendering (PyVista's default and most reliable); ``"client"`` renders
+#: in-browser with vtk.js.  Override with ``GSIM_TRAME_BACKEND``.
+_TRAME_BACKEND = os.environ.get("GSIM_TRAME_BACKEND", "trame").strip().lower()
+
+
+def set_trame_backend(backend: Literal["trame", "client"]) -> None:
+    """Set the trame backend used for notebook live views.
+
+    ``"trame"`` (default) uses server-side rendering; ``"client"`` renders
+    in-browser with vtk.js.  Also configurable via the ``GSIM_TRAME_BACKEND``
+    environment variable.
+    """
+    global _TRAME_BACKEND  # noqa: PLW0603
+    if backend not in ("trame", "client"):
+        msg = f"backend must be 'trame' or 'client', got {backend!r}"
+        raise ValueError(msg)
+    _TRAME_BACKEND = backend
+
+
+#: Master switch for interactive (live) PyVista views.  Off by default: every
+#: plot renders to a static image.  When enabled via :func:`set_interactive_mode`,
+#: interactive views are allowed: in a notebook each interactive plot renders as
+#: its own widget on a single shared trame server; outside a notebook the plot
+#: opens a blocking desktop window.  All live views stay registered until closed
+#: with :func:`close_interactive_views` (or :func:`close_interactive_view`).
+_INTERACTIVE_MODE = False
+
+
+def set_interactive_mode(enabled: bool) -> None:
+    """Enable or disable interactive (live) PyVista views.
+
+    Defaults to ``False``: every plot renders to a static image.  When
+    enabled, interactive views are allowed.  In a notebook each interactive
+    plot renders as its own widget on a single shared trame server, so several
+    views can stay open at once; outside a notebook the plot opens a blocking
+    desktop window.  Close the open views with :func:`close_interactive_views`.
+
+    An explicit per-call ``mode="live"`` (or ``GSIM_VIZ_MODE=live``) always
+    overrides the flag.
+    """
+    global _INTERACTIVE_MODE  # noqa: PLW0603
+    _INTERACTIVE_MODE = bool(enabled)
+
+
+def interactive_mode() -> bool:
+    """Return whether interactive (live) PyVista views are currently enabled."""
+    return _INTERACTIVE_MODE
+
+
+# -- Headless-safe PyVista initialisation ------------------------------------
+def _is_headless() -> bool:
+    """Return ``True`` when no usable X display is available.
+
+    An explicit ``GSIM_FORCE_OFFSCREEN=1`` always forces off-screen
+    rendering, which is useful in CI where a display may be present but X
+    forwarding is undesirable.
+    """
+    if os.environ.get("GSIM_FORCE_OFFSCREEN") == "1":
+        return True
+    return not os.environ.get("DISPLAY")
+
+
+def _start_xvfb() -> None:
+    """Start a virtual frame buffer when ``pyvirtualdisplay`` is available."""
+    try:
+        from pyvirtualdisplay import Display  # pyright: ignore[reportMissingImports]
+
+        display = Display(visible=False, size=(1440, 900))
+        display.start()
+    except Exception:  # optional dependency / headless host
+        logger.warning("pyvirtualdisplay not available; continuing without Xvfb")
+
+
+def _ensure_pyvista():
+    """Import PyVista, forcing off-screen rendering only when headless.
+
+    When a usable ``DISPLAY`` is present normal rendering is left untouched
+    so interactive windows work.  In headless contexts PyVista runs
+    off-screen (optionally backed by a virtual frame buffer), which is what
+    tests and CI rely on.  ``GSIM_FORCE_OFFSCREEN=1`` always forces
+    off-screen rendering.
+    """
+    headless = _is_headless() or _VIZ_MODE == "static"
+    if headless:
+        os.environ.pop("DISPLAY", None)
+        os.environ.setdefault("VTK_DEFAULT_RENDER_WINDOW_OFFSCREEN", "1")
+
+    import warnings
+
+    import pyvista as pv
+
+    if headless:
+        pv.OFF_SCREEN = True
+        try:
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore")
+                _start_xvfb()
+        except Exception:
+            pass
+    return pv
+
+
+pv = _ensure_pyvista()
+
 
 # ---------------------------------------------------------------------------
 # Public API
@@ -28,9 +153,10 @@ def plot_mesh(
     msh_path: str | Path,
     output: str | Path | None = None,
     show_groups: list[str] | None = None,
-    interactive: bool = True,
+    interactive: bool | None = None,
     style: Literal["wireframe", "solid"] = "wireframe",
     transparent_groups: list[str] | None = None,
+    mode: RenderMode = "auto",
 ) -> None:
     """Plot a ``.msh`` mesh using PyVista.
 
@@ -44,14 +170,23 @@ def plot_mesh(
 
     Args:
         msh_path: Path to ``.msh`` file.
-        output: Output PNG path (only used when ``interactive=False``).
+        output: Output PNG path (only used when rendering statically).
         show_groups: Group-name patterns to display (``None`` -> all).
             Example: ``["metal", "P"]`` to show metal layers and ports.
-        interactive: If ``True``, open an interactive 3-D viewer.
-            If ``False``, save a static PNG to *output*.
+        interactive: If ``True``, force an interactive view: in a notebook
+            this renders as a widget on the single shared trame server (so
+            several views can coexist); otherwise it opens a blocking window.
+            ``False`` forces a static PNG.  ``None`` (default) follows the
+            session flag from :func:`set_interactive_mode` — off by default,
+            so plots render statically until it is enabled.
         style: ``"wireframe"`` or ``"solid"``.
         transparent_groups: Group names rendered at low opacity in
             *solid* mode.  Ignored in *wireframe* mode.
+        mode: Rendering mode: ``"auto"`` (default), ``"live"`` or ``"static"``.
+            Overrides ``GSIM_VIZ_MODE`` for this call.  By default interactive
+            views are off; enable them globally with
+            :func:`set_interactive_mode`.  Close open views with
+            :func:`close_interactive_views`.
 
     Example:
         >>> pa.plot_mesh("./sim/palace.msh", show_groups=["metal", "P"])
@@ -67,6 +202,7 @@ def plot_mesh(
             output=output,
             interactive=interactive,
             transparent_groups=transparent_groups or [],
+            mode=mode,
         )
     else:
         _plot_wireframe(
@@ -74,6 +210,7 @@ def plot_mesh(
             output=output,
             show_groups=show_groups,
             interactive=interactive,
+            mode=mode,
         )
 
 
@@ -87,14 +224,15 @@ def _plot_wireframe(
     *,
     output: str | Path | None,
     show_groups: list[str] | None,
-    interactive: bool,
+    interactive: bool | None,
+    mode: RenderMode = "auto",
 ) -> None:
     """Wireframe renderer — one colour per matched group."""
     mio = meshio.read(msh_path)
     group_map: dict[int, str] = {tag: name for name, (tag, _) in mio.field_data.items()}
 
     mesh = cast(pv.DataSet, pv.read(msh_path))  # ty: ignore[redundant-cast]
-    plotter = cast(Any, _make_plotter(interactive))  # ty: ignore[redundant-cast]
+    plotter = cast(Any, _make_plotter(interactive, mode=mode))  # ty: ignore[redundant-cast]
 
     if show_groups:
         ids = [
@@ -118,7 +256,19 @@ def _plot_wireframe(
     else:
         plotter.add_mesh(mesh, style="wireframe", color="black", line_width=1)
 
-    _finish(plotter, msh_path, output=output, interactive=interactive)
+    reset_camera = True
+    axis_idx = _dataset_is_planar(mesh)
+    if axis_idx is not None:
+        _apply_front_camera(plotter, np.asarray(mesh.points), axis_idx)
+        reset_camera = False
+    _finish(
+        plotter,
+        msh_path,
+        output=output,
+        interactive=interactive,
+        mode=mode,
+        reset_camera=reset_camera,
+    )
 
 
 # ---------------------------------------------------------------------------
@@ -204,8 +354,9 @@ def _plot_solid(
     msh_path: Path,
     *,
     output: str | Path | None,
-    interactive: bool,
+    interactive: bool | None,
     transparent_groups: list[str],
+    mode: RenderMode = "auto",
 ) -> None:
     """Solid renderer — coloured surfaces per physical group."""
     mio = meshio.read(msh_path)
@@ -232,7 +383,7 @@ def _plot_solid(
         else:
             cell_blocks_3d.append((block_cells, pv_type, tags))
 
-    active_blocks = cell_blocks_2d if cell_blocks_2d else cell_blocks_3d
+    active_blocks = cell_blocks_2d or cell_blocks_3d
 
     if not active_blocks:
         logger.warning("No supported solid cell blocks — falling back to wireframe.")
@@ -282,7 +433,7 @@ def _plot_solid(
     transparent_mask = np.isin(plain_names, transparent_groups)
     opaque_mask = ~transparent_mask
 
-    plotter = cast(Any, _make_plotter(interactive))  # ty: ignore[redundant-cast]
+    plotter = cast(Any, _make_plotter(interactive, mode=mode))  # ty: ignore[redundant-cast]
 
     # Opaque surfaces with categorical colour map -------------------------
     if np.any(opaque_mask):
@@ -331,7 +482,19 @@ def _plot_solid(
     if transparent_legend_entries:
         plotter.add_legend(transparent_legend_entries, bcolor="white", border=True)
 
-    _finish(plotter, msh_path, output=output, interactive=interactive)
+    reset_camera = True
+    axis_idx = _dataset_is_planar(grid)
+    if axis_idx is not None:
+        _apply_front_camera(plotter, np.asarray(grid.points), axis_idx)
+        reset_camera = False
+    _finish(
+        plotter,
+        msh_path,
+        output=output,
+        interactive=interactive,
+        mode=mode,
+        reset_camera=reset_camera,
+    )
 
 
 # ---------------------------------------------------------------------------
@@ -339,39 +502,330 @@ def _plot_solid(
 # ---------------------------------------------------------------------------
 
 
-def _make_plotter(interactive: bool) -> Any:
+# Live (interactive) PyVista plotters currently held open, keyed by plotter id.
+# Keeping the plotters referenced keeps their render windows / trame viewers
+# alive.  In a notebook every interactive plot adds its own widget to the
+# single shared trame server; outside a notebook a live plot blocks the
+# process until its window is closed.
+_LIVE_PLOTTERS: dict[str, Any] = {}
+
+
+def _view_id(plotter: Any) -> str:
+    """Return a stable registry key for a PyVista plotter."""
+    name = getattr(plotter, "_id_name", None)
+    if name is not None:
+        return str(name)
+    return f"plotter-{id(plotter)}"
+
+
+@contextlib.contextmanager
+def _quiet_trame_logging() -> Any:
+    """Raise trame server/client loggers above INFO while a live view is built.
+
+    trame's state/translator machinery logs the full Vue template
+    tokenisation at INFO on every widget render — ``js_key``/``trigger()``/
+    ``before:``/``after:``/``token`` lines — which floods notebook consoles
+    with hundreds of lines per view.  These are debugging logs, so they are
+    suppressed while the live view widget is created and restored afterwards.
+    """
+    noisy = (
+        "trame",
+        "trame_client",
+        "trame_server",
+        "trame_vtk",
+        "trame_vuetify",
+    )
+    previous: dict[str, int] = {}
+    for name in noisy:
+        lg = logging.getLogger(name)
+        previous[name] = lg.level
+        lg.setLevel(max(int(lg.level), logging.WARNING))
+    try:
+        yield
+    finally:
+        for name, level in previous.items():
+            logging.getLogger(name).setLevel(level)
+
+
+def _in_notebook() -> bool:
+    """Return ``True`` when running inside a Jupyter/IPython kernel."""
+    try:
+        import scooby
+
+        return bool(scooby.in_ipykernel())
+    except Exception:
+        return False
+
+
+def _close_live_views() -> None:
+    """Close every currently open live view and clear the registry."""
+    for view_id, plotter in list(_LIVE_PLOTTERS.items()):
+        try:
+            plotter.close()
+        except Exception:
+            logger.warning("Failed to close live view '%s'", view_id, exc_info=True)
+    _LIVE_PLOTTERS.clear()
+
+
+def close_interactive_views() -> None:
+    """Close every interactive (live) view opened in this process.
+
+    Interactive views are registered while they stay open (see
+    :func:`set_interactive_mode`); calling this releases their render windows
+    and trame server resources.
+    """
+    _close_live_views()
+
+
+def close_interactive_view(view_id: str) -> None:
+    """Close a single interactive view by its plotter id.
+
+    Args:
+        view_id: Plotter id as used in the live-view registry (see
+            :func:`interactive_views`).
+    """
+    plotter = _LIVE_PLOTTERS.pop(view_id, None)
+    if plotter is None:
+        logger.warning("No interactive view registered with id %r", view_id)
+        return
+    try:
+        plotter.close()
+    except Exception:
+        logger.warning("Failed to close interactive view '%s'", view_id, exc_info=True)
+
+
+def interactive_views() -> tuple[str, ...]:
+    """Return the ids of all interactive views currently held open."""
+    return tuple(_LIVE_PLOTTERS)
+
+
+def _dataset_is_planar(dataset: pv.DataSet) -> int | None:
+    """Return the axis index a dataset is thin along (a 2D plane), else ``None``."""
+    bounds = np.asarray(dataset.bounds, dtype=float).reshape(3, 2)
+    span = bounds[:, 1] - bounds[:, 0]
+    span_ref = max(float(np.max(span)), 1.0)
+    thin = np.where(span <= 1e-9 * span_ref)[0]
+    if thin.size == 1:
+        return int(thin[0])
+    return None
+
+
+def _apply_front_camera(plotter: Any, points: np.ndarray, axis_idx: int) -> None:
+    """Point a plotter camera straight at a planar point cloud.
+
+    The camera is positioned along the plane's normal *axis_idx*, facing the
+    centre of the point cloud, with the plot's vertical axis aligned to the
+    in-plane axis so the result is not rolled.
+    """
+    axes = [i for i in range(3) if i != axis_idx]
+    h = points[:, axes[0]]
+    v = points[:, axes[1]]
+    center = ((h.min() + h.max()) / 2, (v.min() + v.max()) / 2)
+    span = (h.max() - h.min(), v.max() - v.min())
+    dist = max(span) * 2.5 if max(span) > 0 else 1.0
+    normal_origin = float(points[:, axis_idx].min())
+    focal = [0.0, 0.0, 0.0]
+    focal[axes[0]] = center[0]
+    focal[axes[1]] = center[1]
+    focal[axis_idx] = normal_origin
+    position = list(focal)
+    position[axis_idx] += dist
+    up = [0.0, 0.0, 0.0]
+    up[axes[1]] = 1.0
+    plotter.camera.focal_point = focal
+    plotter.camera.position = position
+    plotter.camera.up = up
+
+
+def _mode_for(mode: RenderMode) -> RenderMode:
+    """Resolve the effective rendering mode for a plot.
+
+    ``auto`` renders statically unless interactive mode is enabled via
+    :func:`set_interactive_mode`, in which case live rendering is used.  In a
+    notebook, live plots share a single trame server (one widget per plot);
+    outside a notebook a live plot opens a blocking desktop window.
+    ``GSIM_VIZ_MODE=live`` forces live rendering; ``GSIM_VIZ_MODE=static``
+    (or ``none``/``off``) forces static rendering globally.
+    """
+    if mode != "auto":
+        return mode
+    if _VIZ_MODE == "live":
+        return "live"
+    if _INTERACTIVE_MODE and _VIZ_MODE not in ("static", "none", "off"):
+        return "live"
+    return "static"
+
+
+def _want_live(interactive: bool | None, mode: RenderMode) -> bool:
+    """Return whether a plot should be shown live.
+
+    ``interactive=True`` forces a live view (unless an explicit ``mode`` /
+    ``GSIM_VIZ_MODE`` static override is in force).  ``interactive=False``
+    forces a static screenshot.  ``interactive=None`` (default) follows the
+    session flag from :func:`set_interactive_mode` — off by default.
+    """
+    if interactive is False:
+        return False
+    if _mode_for(mode) == "live":
+        return True
+    return (
+        interactive is True
+        and mode == "auto"
+        and _VIZ_MODE not in ("static", "none", "off")
+    )
+
+
+def _make_plotter(interactive: bool | None, *, mode: RenderMode = "auto") -> Any:
     """Create a PyVista plotter with standard window settings."""
-    if interactive:
-        plotter = pv.Plotter(window_size=[1200, 900])
+    pv = _ensure_pyvista()
+    off_screen = not _want_live(interactive, mode)
+    density = {"window_size": [1200, 900]}
+    if off_screen:
+        plotter = pv.Plotter(off_screen=True, **density)
     else:
-        plotter = pv.Plotter(off_screen=True, window_size=[1200, 900])
-    plotter.set_background("white")  # type: ignore[arg-type]  # ty: ignore[invalid-argument-type]
+        plotter = pv.Plotter(**density)
+    plotter.set_background("white")
     return plotter
 
 
+def _show_static(plotter: Any) -> None:
+    """Render a plotter to a temporary PNG and display it inline.
+
+    Used as a fallback when an interactive trame widget cannot be created, so
+    the plot is still shown rather than silently dropped.
+    """
+    dest = _default_output(None, ".png")
+    with contextlib.suppress(Exception):
+        plotter.render()
+    try:
+        plotter.screenshot(str(dest))
+    except Exception:
+        logger.warning("Failed to render fallback static image", exc_info=True)
+        dest = None
+    finally:
+        with contextlib.suppress(Exception):
+            plotter.close()
+    if dest is not None and dest.exists():
+        _disp_img(dest)
+
+
+def _show_live(plotter: Any) -> None:
+    """Show a plotter live and register it in the open-views registry.
+
+    In a notebook the plot is rendered as an interactive widget on the single
+    shared trame server (server-side rendering by default, see
+    :func:`set_trame_backend`), so any number of interactive views can coexist
+    on one server.  PyVista displays the widget itself; this function only
+    renders the scene first and keeps the plotter alive in the registry.  If
+    the widget cannot be created, a static image is shown instead.  Outside a
+    notebook a blocking desktop window is opened, replacing any previously
+    open live view.
+    """
+    if _in_notebook() and getattr(plotter, "notebook", False):
+        try:
+            plotter.render()
+            with _quiet_trame_logging():
+                plotter.show(jupyter_backend=_TRAME_BACKEND)
+        except Exception:
+            logger.warning(
+                "Failed to render interactive trame widget; showing a static image",
+                exc_info=True,
+            )
+            _show_static(plotter)
+            return
+        _LIVE_PLOTTERS[_view_id(plotter)] = plotter
+        return
+    _close_live_views()
+    plotter.show()
+    _LIVE_PLOTTERS[_view_id(plotter)] = plotter
+
+
+def _show_or_screenshot(
+    plotter: Any,
+    *,
+    msh_path: Path | None = None,
+    output: str | Path | None = None,
+    interactive: bool | None,
+    mode: RenderMode = "auto",
+    suffix: str = ".png",
+    reset_camera: bool = True,
+) -> None:
+    """Show a plotter live, or screenshot it, and clean up.
+
+    Interactive (live) views are disabled by default; enable them globally
+    with :func:`set_interactive_mode` or force them per call by passing
+    ``interactive=True``.  When the plot is shown live it is registered in
+    the open-views registry (see :func:`interactive_views`): in a notebook it
+    renders as its own widget on the single shared trame server, so several
+    views can coexist; outside a notebook it opens a blocking desktop window,
+    replacing any previously open live view.  Close open views with
+    :func:`close_interactive_views`.
+
+    Otherwise the plot is rendered to a static PNG and displayed inline.
+
+    When *reset_camera* is ``True`` (default) the camera is reset to an
+    isometric view; pass ``False`` to preserve a camera already configured on
+    the plotter (used by ``plot_fields_2d`` to face the slice plane).
+    """
+    if reset_camera:
+        plotter.camera_position = "iso"
+    plotter.show_axes()
+
+    if _want_live(interactive, mode):
+        _show_live(plotter)
+        return
+
+    # Static screenshot: either interactive=False or the effective mode is
+    # "static".
+    dest = output if output is not None else _default_output(msh_path, suffix)
+    plotter.screenshot(str(dest))
+    plotter.close()
+    _disp_img(Path(dest))
+
+
+def _default_output(msh_path: Path | None, suffix: str) -> Path:
+    """Return the default screenshot path for a plot.
+
+    Uses the mesh path with a new suffix, or a fresh temporary file when no
+    mesh path is available.
+    """
+    if msh_path is not None:
+        return msh_path.with_suffix(suffix)
+    import tempfile
+
+    with tempfile.NamedTemporaryFile(suffix=suffix, delete=False) as tmp:
+        name = tmp.name
+    return Path(name)
+
+
+def _disp_img(path: Path) -> None:
+    """Display a saved image inline when running inside IPython."""
+    try:
+        from IPython.display import Image, display
+
+        display(Image(str(path)))
+    except ImportError:
+        logger.info("Saved plot to %s", path)
+
+
 def _finish(
     plotter: Any,
     msh_path: Path,
     *,
-    output: str | Path | None,
-    interactive: bool,
+    output: str | Path | None = None,
+    interactive: bool | None,
+    mode: RenderMode = "auto",
+    reset_camera: bool = True,
 ) -> None:
     """Show or screenshot the plotter and clean up."""
-    plotter.camera_position = "iso"
-    plotter.show_axes()
-    if interactive:
-        plotter.show()
-    else:
-        if output is None:
-            output = msh_path.with_suffix(".png")
-        plotter.screenshot(str(output))
-        plotter.close()
-        try:
-            from IPython.display import Image, display
-
-            display(Image(str(output)))
-        except ImportError:
-            logger.info("Saved mesh plot to %s", output)
+    _show_or_screenshot(
+        plotter,
+        msh_path=msh_path,
+        output=output,
+        interactive=interactive,
+        mode=mode,
+        reset_camera=reset_camera,
+    )
 
 
 def _color_for_group(name: str) -> str:
diff --git a/tests/common/conftest.py b/tests/common/conftest.py
index ff74e4a6..e523882a 100644
--- a/tests/common/conftest.py
+++ b/tests/common/conftest.py
@@ -1,7 +1,19 @@
-"""Activate the generic PDK for tests in gsim.common that build components."""
+"""Activate the generic PDK for tests in gsim.common that build components.
+
+Activation happens before every test (autouse fixture) rather than only at
+collection time: Palace tests (e.g. the IHP mesh-regression suite) switch the
+active PDK during execution and never restore it, so module-level activation
+alone lets the IHP PDK leak into later ``gsim.common`` tests under the random
+test ordering used by ``pytest-randomly``.
+"""
 
 from __future__ import annotations
 
 import gdsfactory as gf
+import pytest
+
 
-gf.gpdk.PDK.activate()
+@pytest.fixture(autouse=True)
+def _generic_pdk_active() -> None:
+    """Ensure the generic PDK is active for each test."""
+    gf.gpdk.PDK.activate()
diff --git a/tests/common/test_cross_section.py b/tests/common/test_cross_section.py
index 53cd865e..cfd39260 100644
--- a/tests/common/test_cross_section.py
+++ b/tests/common/test_cross_section.py
@@ -1,21 +1,25 @@
-"""Tests for gsim.common.cross_section."""
+"""Tests for gsim.common.cross_section and doping-profile helpers."""
 
 from __future__ import annotations
 
 from dataclasses import FrozenInstanceError
 from typing import Literal
 
+import gdsfactory as gf
 import pytest
 
 from gsim.common.cross_section import (
     PolygonXY2D,
     Rect2D,
     RectYZ2D,
+    build_doped_cross_section,
+    build_optical_cross_section,
     extract_plane_section,
     extract_xy_polygons,
     extract_xz_rectangles,
     extract_yz_rectangles,
 )
+from gsim.common.stack.doping import make_doping_profile
 
 
 def _layer(
@@ -307,3 +311,303 @@ def test_extract_plane_section_dispatch(self):
 
         assert len(z_polys) == 1
         assert isinstance(z_polys[0], PolygonXY2D)
+
+
+def _centered_rect(wx: float, wy: float, layer: tuple[int, int]):
+    import gdsfactory as gf
+
+    r = gf.Component()
+    r << gf.c.rectangle((wx, wy), centered=True, layer=layer)
+    return r
+
+
+class TestBuildDopedCrossSection:
+    """Tests for build_doped_cross_section() using the active PDK stack."""
+
+    def _build_component(self):
+        import gdsfactory as gf
+
+        LAYER = gf.gpdk.LAYER
+        comp = gf.Component()
+        wg = comp << _centered_rect(10.0, 0.4, LAYER.WG)
+        wg.y = -20.0
+        return comp, LAYER
+
+    def _doping_result(self, comp, rib_center_y=-20.0):
+        return make_doping_profile(
+            comp,
+            length=10.0,
+            rib_center_y=rib_center_y,
+            rib_width=0.4,
+            profile={"upper": [(2.0, 2e4)], "lower": [(2.0, 2e4)]},
+            sides={
+                "upper": {"base_layer": (23, 0), "name_prefix": "pp_slab_", "sign": 1},
+                "lower": {
+                    "base_layer": (24, 0),
+                    "name_prefix": "npp_slab_",
+                    "sign": -1,
+                },
+            },
+            zmin=0.0,
+            zmax=0.09,
+        )
+
+    def test_builds_stack_with_doping_and_rib_layers(self):
+        comp, LAYER = self._build_component()
+        doping = self._doping_result(comp)
+
+        stack, section = build_doped_cross_section(
+            comp,
+            axis="x",
+            value=0.0,
+            substrate_thickness=2.0,
+            include_substrate=False,
+            doping=doping,
+            metal1=(1.1, 1.0),
+            rib_layers=[
+                ("p_rib", LAYER.P, 1.6e3),
+                ("n_rib", LAYER.N, 1.6e3),
+            ],
+            permittivity=11.9,
+            fmax=200e9,
+            verbose=False,
+        )
+
+        assert "pp_slab_0" in stack.layers
+        assert "npp_slab_0" in stack.layers
+        assert "p_rib" in stack.layers
+        assert "n_rib" in stack.layers
+
+        p_rib = stack.layers["p_rib"]
+        assert p_rib.gds_layer == tuple(LAYER.P)
+        assert p_rib.zmax == pytest.approx(0.22)
+        assert p_rib.thickness == pytest.approx(0.22)
+        assert p_rib.material == "p_rib"
+
+        layers = {r.layer_name for r in section}
+        assert {"core", "pp_slab_0", "npp_slab_0"} <= layers
+
+    def test_metal1_override_applied(self):
+        comp, _LAYER = self._build_component()
+        stack, _ = build_doped_cross_section(
+            comp,
+            axis="x",
+            value=0.0,
+            substrate_thickness=2.0,
+            metal1=(1.1, 1.0),
+            verbose=False,
+        )
+        m1 = stack.layers["metal1"]
+        assert m1.zmin == pytest.approx(1.1)
+        assert m1.zmax == pytest.approx(2.1)
+        assert m1.thickness == pytest.approx(1.0)
+
+    def test_no_doping_no_rib_layers(self):
+        comp, _LAYER = self._build_component()
+        stack, _ = build_doped_cross_section(
+            comp,
+            axis="x",
+            value=0.0,
+            substrate_thickness=2.0,
+            verbose=False,
+        )
+        assert "p_rib" not in stack.layers
+        assert "pp_slab_0" not in stack.layers
+        assert "core" in stack.layers
+
+
+@pytest.fixture
+def doping_sides():
+    return {
+        "upper": {"base_layer": (23, 0), "name_prefix": "pp_slab_", "sign": 1},
+        "lower": {"base_layer": (24, 0), "name_prefix": "npp_slab_", "sign": -1},
+    }
+
+
+def _doping_profile():
+    return {
+        "upper": [(2.0, 2e4), (2.0, 8e4)],
+        "lower": [(2.0, 2e4), (2.0, 8e4)],
+    }
+
+
+def test_make_doping_profile_basic(doping_sides):
+    comp = gf.Component()
+    result = make_doping_profile(
+        comp,
+        length=10.0,
+        rib_center_y=-20.0,
+        rib_width=0.4,
+        profile=_doping_profile(),
+        sides=doping_sides,
+        zmin=0.0,
+        zmax=0.09,
+    )
+
+    expected = {"pp_slab_0", "pp_slab_1", "npp_slab_0", "npp_slab_1"}
+    assert set(result["layer_specs"]) == expected
+    assert set(result["materials"]) == set(result["layer_specs"])
+
+    upper = result["centres"]["upper"]
+    lower = result["centres"]["lower"]
+    rib_upper_edge = -20.0 + 0.4 / 2
+    rib_lower_edge = -20.0 - 0.4 / 2
+    assert upper[0] == pytest.approx(rib_upper_edge + 2.0 / 2)
+    assert upper[1] == pytest.approx(rib_upper_edge + 2.0 + 2.0 / 2)
+    assert lower[0] == pytest.approx(rib_lower_edge - 2.0 / 2)
+    assert lower[1] == pytest.approx(rib_lower_edge - 2.0 - 2.0 / 2)
+
+
+def test_make_doping_profile_layer_spec(doping_sides):
+    comp = gf.Component()
+    result = make_doping_profile(
+        comp,
+        length=10.0,
+        rib_center_y=0.0,
+        rib_width=1.0,
+        profile=_doping_profile(),
+        sides=doping_sides,
+        zmin=0.0,
+        zmax=0.09,
+    )
+
+    layer = result["layer_specs"]["pp_slab_0"]
+    assert layer.gds_layer == (23, 0)
+    assert layer.zmin == 0.0
+    assert layer.zmax == 0.09
+    assert layer.thickness == 0.09
+    assert layer.material == "pp_slab_0"
+
+    assert result["layer_specs"]["pp_slab_1"].gds_layer == (23, 1)
+    assert result["layer_specs"]["npp_slab_0"].gds_layer == (24, 0)
+
+
+def test_make_doping_profile_materials(doping_sides):
+    comp = gf.Component()
+    result = make_doping_profile(
+        comp,
+        length=10.0,
+        rib_center_y=0.0,
+        rib_width=1.0,
+        profile=_doping_profile(),
+        sides=doping_sides,
+        zmin=0.0,
+        zmax=0.09,
+    )
+    assert result["materials"]["pp_slab_0"].conductivity == 2e4
+    assert result["materials"]["pp_slab_1"].conductivity == 8e4
+    assert result["materials"]["npp_slab_1"].conductivity == 8e4
+
+
+def test_make_doping_profile_empty_side(doping_sides):
+    comp = gf.Component()
+    result = make_doping_profile(
+        comp,
+        length=10.0,
+        rib_center_y=0.0,
+        rib_width=1.0,
+        profile={"upper": [], "lower": [(1.0, 1e4)]},
+        sides=doping_sides,
+        zmin=0.0,
+        zmax=0.09,
+    )
+    assert "pp_slab_0" not in result["layer_specs"]
+    assert "npp_slab_0" in result["layer_specs"]
+    assert result["centres"]["upper"] == []
+
+
+def test_make_doping_profile_geometry_added(doping_sides):
+    comp = gf.Component()
+    make_doping_profile(
+        comp,
+        length=10.0,
+        rib_center_y=0.0,
+        rib_width=1.0,
+        profile=_doping_profile(),
+        sides=doping_sides,
+        zmin=0.0,
+        zmax=0.09,
+    )
+    total = len(comp.get_polygons())
+    assert total == 4
+
+
+class TestBuildOpticalCrossSection:
+    """Tests for build_optical_cross_section() — all-Si device in uniform cladding."""
+
+    def _component(self):
+        import gdsfactory as gf
+
+        LAYER = gf.gpdk.LAYER
+        comp = gf.Component()
+        wg = comp << _centered_rect(10.0, 0.4, LAYER.WG)
+        wg.y = -20.0
+        comp << _centered_rect(10.0, 100.0, LAYER.SLAB90)
+        p = comp << gf.c.rectangle((10.0, 0.2), layer=LAYER.P)
+        p.y = -19.9
+        n = comp << gf.c.rectangle((10.0, 0.2), layer=LAYER.N)
+        n.y = -20.1
+        return comp, LAYER
+
+    def _device_layers(self, LAYER):
+        return {
+            "core": (LAYER.WG, 0.0, 0.22),
+            "slab": (LAYER.SLAB90, 0.0, 0.09),
+            "p_rib": (LAYER.P, 0.0, 0.22),
+            "n_rib": (LAYER.N, 0.0, 0.22),
+        }
+
+    def test_builds_all_dielectric_stack(self):
+        comp, LAYER = self._component()
+        stack, section = build_optical_cross_section(
+            comp,
+            axis="x",
+            value=0.0,
+            device_layers=self._device_layers(LAYER),
+            substrate_thickness=2.0,
+            cladding_top=2.0,
+            verbose=False,
+        )
+
+        assert set(stack.layers) == {"core", "slab", "p_rib", "n_rib"}
+
+        # Every device region is plain silicon — no Drude-doped materials.
+        for layer in stack.layers.values():
+            assert layer.material == "si"
+            assert layer.layer_type == "dielectric"
+
+        # PN junction shares the rib's z-extent.
+        assert stack.layers["p_rib"].gds_layer == tuple(LAYER.P)
+        assert stack.layers["n_rib"].gds_layer == tuple(LAYER.N)
+        assert stack.layers["p_rib"].zmax == pytest.approx(0.22)
+
+        # Uniform cladding: a single SiO2 dielectric spanning the whole domain.
+        assert len(stack.dielectrics) == 1
+        oxide = stack.dielectrics[0]
+        assert oxide["name"] == "oxide"
+        assert oxide["material"] == "sio2"
+        assert oxide["zmin"] == pytest.approx(-2.0)
+        assert oxide["zmax"] == pytest.approx(2.0)
+
+        # Materials DB populated so Palace can resolve them.
+        assert "si" in stack.materials
+        assert "sio2" in stack.materials
+
+        layer_names = {r.layer_name for r in section}
+        assert {"core", "slab", "p_rib", "n_rib"} <= layer_names
+        assert all(r.material == "si" for r in section)
+
+    def test_uniform_cladding_ranges(self):
+        comp, LAYER = self._component()
+        stack, _ = build_optical_cross_section(
+            comp,
+            axis="x",
+            value=0.0,
+            device_layers=self._device_layers(LAYER),
+            substrate_thickness=3.0,
+            cladding_top=1.5,
+            verbose=False,
+        )
+        oxide = stack.dielectrics[0]
+        assert oxide["zmin"] == pytest.approx(-3.0)
+        assert oxide["zmax"] == pytest.approx(1.5)
diff --git a/tests/common/test_doping_materials.py b/tests/common/test_doping_materials.py
new file mode 100644
index 00000000..f610e068
--- /dev/null
+++ b/tests/common/test_doping_materials.py
@@ -0,0 +1,75 @@
+"""Tests for the generic doped-material builders.
+
+These helpers must be free of hardcoded / PDK-specific values so they can be
+reused across projects.
+"""
+
+from __future__ import annotations
+
+import pytest
+
+from gsim.common.stack.materials import (
+    DispersionModel,
+    ValidityRange,
+    make_doped_material,
+    make_doped_materials,
+)
+
+
+class TestMakeDopedMaterial:
+    def test_defaults(self):
+        mat = make_doped_material("p_rib", 1.6e3)
+        assert mat.conductivity == 1.6e3
+        assert mat.permittivity == 11.9
+        assert len(mat.dispersion_models) == 1
+        model = mat.dispersion_models[0]
+        assert isinstance(model, DispersionModel)
+        assert model.type == "constant"
+        assert model.permittivity == 11.9
+        assert model.validity == ValidityRange(valid_frequency=(0, 200e9))
+        assert model.source == "doped Si (p_rib) -- Drude sigma"
+
+    def test_custom_values(self):
+        mat = make_doped_material(
+            "a", 5e4, permittivity=12.0, fmax=50e9, source="custom"
+        )
+        assert mat.permittivity == 12.0
+        assert mat.dispersion_models[0].validity == ValidityRange(
+            valid_frequency=(0, 50e9)
+        )
+        assert mat.dispersion_models[0].source == "custom"
+
+    def test_resolves_to_conductive_at_rf(self):
+        mat = make_doped_material("x", 2e4)
+        resolved = mat.evaluate_at_wavelength(1000.0)  # RF-ish wavelength
+        assert resolved.conductivity == 2e4
+        assert resolved.behavior == "conductive"
+
+
+class TestMakeDopedMaterials:
+    def test_dict_input(self):
+        mats = make_doped_materials({"pp_slab_0": 2e4, "pp_slab_1": 8e4})
+        assert set(mats) == {"pp_slab_0", "pp_slab_1"}
+        assert mats["pp_slab_0"].conductivity == 2e4
+        assert mats["pp_slab_1"].conductivity == 8e4
+
+    def test_two_tuple_input(self):
+        mats = make_doped_materials([("n_rib", 1.6e3), ("p_rib", 1.6e3)])
+        assert mats["n_rib"].permittivity == 11.9
+        assert mats["n_rib"].conductivity == 1.6e3
+
+    def test_four_tuple_input(self):
+        mats = make_doped_materials([("r1", 13.0, 7e3, "doc")])
+        assert mats["r1"].permittivity == 13.0
+        assert mats["r1"].conductivity == 7e3
+        assert mats["r1"].dispersion_models[0].source == "doc"
+
+    def test_invalid_entry(self):
+        with pytest.raises(ValueError):
+            make_doped_materials([("only_name",)])
+
+    def test_returned_materials_resolvable(self):
+        mats = make_doped_materials({"a": 1e4})
+        # The generated object behaves like any database material.
+        for mat in mats.values():
+            assert mat.evaluate_at_frequency(1e9).behavior == "conductive"
diff --git a/tests/palace/test_config_dispersion.py b/tests/palace/test_config_dispersion.py
index ac765769..c7b3acb3 100644
--- a/tests/palace/test_config_dispersion.py
+++ b/tests/palace/test_config_dispersion.py
@@ -2,12 +2,16 @@
 
 from __future__ import annotations
 
+import json
+
 import pytest
 from scipy.constants import c as C0  # noqa: N812
 
+from gsim.common.stack.extractor import Layer, LayerStack
 from gsim.common.stack.materials import MATERIALS_DB
 from gsim.palace.materials import resolve_palace_materials_at_frequency
-from gsim.palace.models import DrivenConfig
+from gsim.palace.mesh.config_generator import generate_palace_config
+from gsim.palace.models import BoundaryModeConfig, DrivenConfig
 
 
 class TestDrivenConfigCenterFrequency:
@@ -104,3 +108,98 @@ def test_sapphire_anisotropic_resolved(self):
         resolved = resolve_palace_materials_at_frequency(materials, freq_hz)
         assert "sapphire" in resolved
         assert isinstance(resolved["sapphire"]["permittivity"], list)
+
+
+class TestBoundaryModeFrequencyResolution:
+    """Boundary-mode configs must evaluate dispersion at the operating frequency."""
+
+    @staticmethod
+    def _stack_with_core() -> LayerStack:
+        stack = LayerStack()
+        stack.layers["CORE"] = Layer(
+            name="CORE",
+            gds_layer=(1, 0),
+            zmin=0.0,
+            zmax=0.22,
+            thickness=0.22,
+            material="silicon",
+            layer_type="dielectric",
+        )
+        stack.materials = {"silicon": MATERIALS_DB["silicon"].to_dict()}
+        return stack
+
+    @staticmethod
+    def _groups() -> dict:
+        return {
+            "volumes": {
+                "CORE": {
+                    "phys_group": 101,
+                    "is_shaped_dielectric": True,
+                }
+            },
+            "conductor_surfaces": {},
+            "pec_surfaces": {},
+            "port_surfaces": {},
+            "boundary_surfaces": {},
+        }
+
+    def _material_permittivity(self, config_path) -> float:
+        config = json.loads(config_path.read_text())
+        materials = config["Domains"]["Materials"]
+        core_mat = next(
+            entry for entry in materials if 101 in entry.get("Attributes", [])
+        )
+        return core_mat["Permittivity"]
+
+    def test_optical_frequency_uses_sellmeier(self, tmp_path):
+        """At 1550 nm the config permittivity matches Sellmeier silicon (n~3.48)."""
+        boundary = BoundaryModeConfig(freq=C0 / (1.55e-6), num_modes=2, save=1)
+        config_path = generate_palace_config(
+            groups=self._groups(),
+            ports=[],
+            port_info=[],
+            stack=self._stack_with_core(),
+            output_path=tmp_path,
+            model_name="palace",
+            fmax=100e9,
+            simulation_type="boundarymode",
+            boundary_mode_config=boundary,
+            absorbing_boundary=False,
+        )
+        eps = self._material_permittivity(config_path)
+        assert eps == pytest.approx(12.09, abs=0.05)
+
+    def test_rf_frequency_uses_constant_model(self, tmp_path):
+        """At 50 GHz the config permittivity falls back to the RF constant value."""
+        boundary = BoundaryModeConfig(freq=50e9, num_modes=2, save=1)
+        config_path = generate_palace_config(
+            groups=self._groups(),
+            ports=[],
+            port_info=[],
+            stack=self._stack_with_core(),
+            output_path=tmp_path,
+            model_name="palace",
+            fmax=100e9,
+            simulation_type="boundarymode",
+            boundary_mode_config=boundary,
+            absorbing_boundary=False,
+        )
+        eps = self._material_permittivity(config_path)
+        assert eps == pytest.approx(11.9)
+
+    def test_no_frequency_resolution_without_boundary_config(self, tmp_path):
+        """Without a boundary-mode config, stack materials pass through unchanged."""
+        stack = self._stack_with_core()
+        stack.materials = {"silicon": {"permittivity": 12.1}}
+        config_path = generate_palace_config(
+            groups=self._groups(),
+            ports=[],
+            port_info=[],
+            stack=stack,
+            output_path=tmp_path,
+            model_name="palace",
+            fmax=100e9,
+            simulation_type="boundarymode",
+            absorbing_boundary=False,
+        )
+        assert self._material_permittivity(config_path) == pytest.approx(12.1)
diff --git a/tests/palace/test_field_viz.py b/tests/palace/test_field_viz.py
index e138ca3b..b58335bb 100644
--- a/tests/palace/test_field_viz.py
+++ b/tests/palace/test_field_viz.py
@@ -2,6 +2,8 @@
 
 from __future__ import annotations
 
+from typing import Any
+
 import matplotlib as mpl
 import numpy as np
 import pytest
@@ -31,18 +33,16 @@ def planar_vector_dataset() -> pv.DataSet:
 
 
 def test_plot_fields_2d_dataset_smoke(planar_vector_dataset: pv.DataSet) -> None:
-    """Matplotlib plotting utility should render from a dataset source."""
-    fig, ax, out = field_viz.plot_fields_2d(
+    """PyVista plotting utility should render from a dataset source."""
+    plotter = field_viz.plot_fields_2d(
         planar_vector_dataset,
         normal="z",
         origin=0.0,
         show=False,
     )
 
-    assert fig is not None
-    assert ax is not None
-    assert out.u.shape == out.v.shape
-    fig.clf()
+    assert isinstance(plotter, pv.Plotter)
+    plotter.close()
 
 
 def test_plot_fields_2d_loads_from_source(
@@ -67,7 +67,7 @@ def _fake_load_fields(
 
     monkeypatch.setattr(field_viz, "load_fields", _fake_load_fields)
 
-    fig, _, _ = field_viz.plot_fields_2d(
+    plotter = field_viz.plot_fields_2d(
         "dummy-output-dir",
         excitation=3,
         cycle=7,
@@ -83,7 +83,7 @@ def _fake_load_fields(
         "cycle": 7,
         "boundary": True,
     }
-    fig.clf()
+    plotter.close()
 
 
 def test_plot_fields_2d_missing_field_raises(planar_vector_dataset: pv.DataSet) -> None:
@@ -98,6 +98,31 @@ def test_plot_fields_2d_missing_field_raises(planar_vector_dataset: pv.DataSet)
         )
 
 
+def test_plot_fields_2d_forwards_interactive_flag(
+    monkeypatch: pytest.MonkeyPatch,
+    planar_vector_dataset: pv.DataSet,
+) -> None:
+    """The ``interactive`` flag is forwarded to the display helper."""
+    import gsim.viz as viz
+
+    captured: dict[str, object] = {}
+
+    def _spy(plotter: Any, **_kwargs: object) -> None:
+        captured["interactive"] = _kwargs.get("interactive")
+        plotter.close()
+
+    monkeypatch.setattr(viz, "_show_or_screenshot", _spy)
+
+    field_viz.plot_fields_2d(
+        planar_vector_dataset,
+        normal="z",
+        origin=0.0,
+        show=True,
+        interactive=False,
+    )
+    assert captured["interactive"] is False
+
+
 def test_extract_streamplot_inputs_2d(planar_vector_dataset: pv.DataSet) -> None:
     """Streamplot input extraction should return PalaceToolkit-style arrays."""
     out = field_viz.extract_streamplot_inputs_2d(
diff --git a/tests/palace/test_mesh_integration.py b/tests/palace/test_mesh_integration.py
index 69023250..bdbc3597 100644
--- a/tests/palace/test_mesh_integration.py
+++ b/tests/palace/test_mesh_integration.py
@@ -11,6 +11,7 @@
 
 import gdsfactory as gf
 import pytest
+from scipy.constants import c as C0  # noqa: N812
 
 from gsim.common import Layer, LayerStack
 from gsim.palace import BoundaryModeSim, DrivenSim
@@ -165,6 +166,63 @@ def test_config_has_non_air_dielectric_materials(self, boundarymode_sim):
         )
 
 
+class TestBoundaryModeBackgroundMaterial:
+    """set_airbox(material=...) retunes the 2D background away from air."""
+
+    @staticmethod
+    def _build(tmp_path, material, freq):
+        component = _make_cpw_component()
+        sim = BoundaryModeSim()
+        sim.set_output_dir(str(tmp_path / "palace-sim-bg"))
+        sim.set_geometry(component)
+        sim.set_stack(substrate_thickness=2.0)
+        sim.set_airbox(
+            material=material,
+            margin_x=5.0,
+            margin_y=5.0,
+            z_above=5.0,
+            z_below=5.0,
+        )
+        sim.set_cross_section("x=0")
+        sim.set_boundary_mode(freq=freq, num_modes=1, save=0)
+        sim.mesh(preset="coarse", verbose=False)
+        return sim
+
+    def test_default_background_is_air(self, tmp_path):
+        """Without a custom material the background volume is named 'air'."""
+        sim = self._build(tmp_path, "air", 10e9)
+        assert "air" in sim._last_mesh_result.groups["volumes"]
+
+    def test_sio2_background_replaces_air(self, tmp_path):
+        """material='sio2' names the background 'sio2' and drops the air volume."""
+        sim = self._build(tmp_path, "sio2", 10e9)
+        volumes = sim._last_mesh_result.groups["volumes"]
+        assert "sio2" in volumes
+        assert "air" not in volumes
+
+    def test_sio2_background_resolves_optical_permittivity(self, tmp_path):
+        """The SiO2 background resolves to the Sellmeier value at 1550 nm."""
+        sim = self._build(tmp_path, "sio2", C0 / 1.55e-6)
+        sim.write_config()
+        config = json.loads((Path(sim._output_dir) / "config.json").read_text())
+
+        volumes = sim._last_mesh_result.groups["volumes"]
+        bg_pg = volumes["sio2"]["phys_group"]
+        materials = config["Domains"]["Materials"]
+        bg_entry = next(m for m in materials if bg_pg in m.get("Attributes", []))
+        assert bg_entry["Permittivity"] == pytest.approx(2.085, abs=0.01)
+
+        # No leftover eps=1.0 background remains.
+        eps_values = [
+            float(m.get("Permittivity", 1.0))
+            for m in materials
+            if isinstance(m.get("Permittivity"), int | float)
+        ]
+        assert not any(abs(e - 1.0) < 1e-9 for e in eps_values), (
+            "Expected no air (eps=1.0) material in the SiO2-clad config"
+        )
+
+
 class TestCPWMeshVolumetricConductors:
     """Test mesh generation with volumetric (non-planar) conductors."""
 
diff --git a/tests/palace/test_plane_section_viz.py b/tests/palace/test_plane_section_viz.py
new file mode 100644
index 00000000..95e21443
--- /dev/null
+++ b/tests/palace/test_plane_section_viz.py
@@ -0,0 +1,102 @@
+"""Tests for gsim.palace.plane_section (2D cross-section physical-group viz)."""
+
+from __future__ import annotations
+
+import matplotlib as mpl
+
+mpl.use("Agg")
+import matplotlib.pyplot as plt
+import pytest
+from matplotlib.patches import Rectangle
+
+from gsim.common.cross_section import PolygonXY2D, Rect2D, RectYZ2D
+from gsim.palace.plane_section import plot_plane_section
+
+
+def _rect_yz(y0, y1, z0, z1, name="rib"):
+    return RectYZ2D(y0=y0, y1=y1, zmin=z0, zmax=z1, layer_name=name, material=name)
+
+
+def _rect_xz(x0, x1, z0, z1, name="rib"):
+    return Rect2D(x0=x0, x1=x1, zmin=z0, zmax=z1, layer_name=name, material=name)
+
+
+class TestPlotPlaneSection:
+    def test_rect_yz(self):
+        fig, ax = plt.subplots()
+        out = plot_plane_section(
+            [_rect_yz(-20, -19.8, 0, 0.22, "p_rib")], ax=ax, legend=False
+        )
+        assert out is ax
+        assert len(ax.patches) == 1
+        patch = ax.patches[0]
+        assert isinstance(patch, Rectangle)
+        assert patch.get_x() == -20
+        assert patch.get_y() == 0
+        assert patch.get_width() == pytest.approx(0.2)
+        assert patch.get_height() == 0.22
+        assert ax.get_xlabel() == "y (um)"
+        assert ax.get_ylabel() == "z (um)"
+        plt.close(fig)
+
+    def test_rect_xz(self):
+        fig, ax = plt.subplots()
+        plot_plane_section([_rect_xz(0, 10, 0, 1, "wg")], ax=ax, legend=False)
+        assert ax.get_xlabel() == "x (um)"
+        assert ax.get_ylabel() == "z (um)"
+        plt.close(fig)
+
+    def test_polygon_xy(self):
+        fig, ax = plt.subplots()
+        poly = PolygonXY2D(
+            exterior=((0, 0), (1, 0), (1, 1), (0, 1)),
+            holes=(),
+            layer_name="core",
+            material="si",
+        )
+        plot_plane_section([poly], ax=ax, legend=False)
+        assert ax.get_xlabel() == "x (um)"
+        assert ax.get_ylabel() == "y (um)"
+        assert len(ax.patches) == 1
+        plt.close(fig)
+
+    def test_custom_colors(self):
+        fig, ax = plt.subplots()
+        plot_plane_section(
+            [_rect_yz(-1, 1, 0, 0.2, "a"), _rect_yz(2, 3, 0, 0.1, "b")],
+            colors={"a": "red", "b": "blue"},
+            ax=ax,
+            legend=False,
+        )
+        assert ax.patches[0].get_facecolor()[:3] == (1.0, 0.0, 0.0)
+        assert ax.patches[1].get_facecolor()[:3] == (0.0, 0.0, 1.0)
+        plt.close(fig)
+
+    def test_auto_limits_and_ranges(self):
+        fig, ax = plt.subplots()
+        plot_plane_section(
+            [_rect_yz(1, 2, 3, 4, "a")],
+            h_range=(0, 10),
+            v_range=(-1, 5),
+            ax=ax,
+            legend=False,
+        )
+        assert ax.get_xlim() == (0, 10)
+        assert ax.get_ylim() == (-1, 5)
+        plt.close(fig)
+
+    def test_legend_deduplicated(self):
+        fig, ax = plt.subplots()
+        plot_plane_section(
+            [_rect_yz(-1, 1, 0, 0.2, "a"), _rect_yz(-2, -1.5, 0, 0.1, "a")],
+            ax=ax,
+        )
+        legend = ax.get_legend()
+        assert legend is not None
+        labels = [t.get_text() for t in legend.get_texts()]
+        assert labels.count("a") == 1
+        plt.close(fig)
+
+    def test_unsupported_element(self):
+        with pytest.raises(TypeError):
+            plot_plane_section([object()])
diff --git a/tests/palace/test_run_local.py b/tests/palace/test_run_local.py
index 64a47630..72ddf7f4 100644
--- a/tests/palace/test_run_local.py
+++ b/tests/palace/test_run_local.py
@@ -6,7 +6,167 @@
 from types import SimpleNamespace
 from typing import cast
 
-from gsim.palace import DrivenSim
+from gsim.palace import BoundaryModeSim, DrivenSim
+from gsim.palace.base import _recommend_parallel
+
+
+def _mesh_result(elements: int, tetrahedra: int = 0, bbox: dict | None = None):
+    """A minimal MeshResult-like object exposing mesh_stats."""
+    stats: dict = {
+        "elements": elements,
+        "nodes": elements,
+    }
+    if tetrahedra:
+        stats["tetrahedra"] = tetrahedra
+    if bbox is not None:
+        stats["bbox"] = bbox
+    return SimpleNamespace(mesh_stats=stats, groups={})
+
+
+def _setup_sim(sim, output_dir: Path) -> None:
+    postpro_dir = output_dir / "output" / "palace"
+    output_dir.mkdir(parents=True)
+    postpro_dir.mkdir(parents=True)
+    (output_dir / "config.json").write_text("{}")
+    (output_dir / "palace.msh").write_text("mesh")
+    sim.set_output_dir(output_dir)
+
+
+def _setup_local_palace(monkeypatch, tmp_path: Path) -> None:
+    """Provide a fake ./bin/palace and resolve it from cwd."""
+    local_bin_dir = tmp_path / "bin"
+    local_bin_dir.mkdir()
+    local_palace = local_bin_dir / "palace"
+    local_palace.write_text("#!/bin/sh\nexit 0\n")
+    local_palace.chmod(0o755)
+    monkeypatch.chdir(tmp_path)
+
+
+def test_recommend_parallel_2d_uses_single_rank_openmp(monkeypatch):
+    """2D mode analysis defaults to 1 MPI rank + OpenMP threads."""
+    monkeypatch.setattr("gsim.palace.base._count_physical_cpus", lambda: 16)
+    procs, threads = _recommend_parallel(
+        {"elements": 50_000}, "boundarymode", None, None
+    )
+    assert procs == 1
+    assert threads == 16
+
+
+def test_recommend_parallel_3d_capped_by_dofs(monkeypatch):
+    """3D runs are capped by problem size and never exceed 4 ranks."""
+    monkeypatch.setattr("gsim.palace.base._count_physical_cpus", lambda: 16)
+    # ~2.5M DOFs, enough for several ranks, but still capped at 4.
+    procs, threads = _recommend_parallel(
+        {"elements": 500_000, "tetrahedra": 500_000}, "driven", None, None
+    )
+    assert procs == 4
+    assert threads is None
+
+    # Tiny 3D problem: only 1 rank.
+    procs, _ = _recommend_parallel(
+        {"elements": 1_000, "tetrahedra": 1_000}, "driven", None, None
+    )
+    assert procs == 1
+
+
+def test_recommend_parallel_respects_explicit_processes(monkeypatch):
+    """An explicit num_processes is kept unchanged."""
+    monkeypatch.setattr("gsim.palace.base._count_physical_cpus", lambda: 16)
+    procs, threads = _recommend_parallel({"elements": 50_000}, "boundarymode", 2, None)
+    assert procs == 2
+    assert threads is None
+
+    procs, threads = _recommend_parallel({"elements": 50_000}, "boundarymode", 1, None)
+    assert procs == 1
+    assert threads == 16  # serial run defaults threads to cores
+
+
+def test_run_local_boundarymode_defaults_to_single_rank(monkeypatch, tmp_path):
+    """BoundaryModeSim.run_local() without args uses -np 1 and -nt <cpus>."""
+    _setup_local_palace(monkeypatch, tmp_path)
+    output_dir = tmp_path / "sim"
+
+    monkeypatch.delenv("PALACE_SIF", raising=False)
+    monkeypatch.delenv("PALACE_EXECUTABLE", raising=False)
+    monkeypatch.setattr("gsim.palace.base._count_physical_cpus", lambda: 8)
+
+    captured: dict[str, object] = {}
+
+    def _fake_run(cmd, **_kwargs):
+        captured["cmd"] = cmd
+        return SimpleNamespace(stdout="", stderr="", returncode=0)
+
+    monkeypatch.setattr("subprocess.run", _fake_run)
+
+    sim = BoundaryModeSim()
+    sim._last_mesh_result = _mesh_result(50_000)
+    _setup_sim(sim, output_dir)
+
+    result = sim.run_local(verbose=False)
+
+    assert isinstance(result, dict)
+    cmd = cast(list[str], captured["cmd"])
+    assert "-np" in cmd
+    assert "1" in cmd[cmd.index("-np") + 1 :][:1]
+    assert "-nt" in cmd
+    assert "8" in cmd[cmd.index("-nt") + 1 :][:1]
+
+
+def test_run_local_explicit_large_processes_warns(monkeypatch, tmp_path, caplog):
+    """Requesting too many ranks for a 2D problem logs a warning."""
+    _setup_local_palace(monkeypatch, tmp_path)
+    output_dir = tmp_path / "sim"
+    monkeypatch.delenv("PALACE_SIF", raising=False)
+    monkeypatch.delenv("PALACE_EXECUTABLE", raising=False)
+    monkeypatch.setattr("gsim.palace.base._count_physical_cpus", lambda: 16)
+
+    captured: dict[str, object] = {}
+
+    def _fake_run(cmd, **_kwargs):
+        captured["cmd"] = cmd
+        return SimpleNamespace(stdout="", stderr="", returncode=0)
+
+    monkeypatch.setattr("subprocess.run", _fake_run)
+
+    sim = BoundaryModeSim()
+    sim._last_mesh_result = _mesh_result(50_000)
+    _setup_sim(sim, output_dir)
+
+    with caplog.at_level("WARNING", logger="gsim.palace.base"):
+        sim.run_local(num_processes=8, verbose=False)
+
+    assert any("does not scale beyond 1 rank" in r.message for r in caplog.records)
+    # The explicit request is still respected.
+    cmd = cast(list[str], captured["cmd"])
+    assert "8" in cmd[cmd.index("-np") + 1 :][:1]
+
+
+def test_run_local_3d_caps_default_processes(monkeypatch, tmp_path):
+    """A 3D DrivenSim default is capped to 4 ranks regardless of cores."""
+    _setup_local_palace(monkeypatch, tmp_path)
+    output_dir = tmp_path / "sim"
+    monkeypatch.delenv("PALACE_SIF", raising=False)
+    monkeypatch.delenv("PALACE_EXECUTABLE", raising=False)
+    monkeypatch.setattr("gsim.palace.base._count_physical_cpus", lambda: 32)
+
+    captured: dict[str, object] = {}
+
+    def _fake_run(cmd, **_kwargs):
+        captured["cmd"] = cmd
+        return SimpleNamespace(stdout="", stderr="", returncode=0)
+
+    monkeypatch.setattr("subprocess.run", _fake_run)
+
+    sim = DrivenSim()
+    sim._last_mesh_result = _mesh_result(1_000_000, tetrahedra=1_000_000)
+    _setup_sim(sim, output_dir)
+
+    result = sim.run_local(verbose=False)
+
+    assert isinstance(result, dict)
+    cmd = cast(list[str], captured["cmd"])
+    assert "-np" in cmd
+    assert "4" in cmd[cmd.index("-np") + 1 :][:1]
 
 
 def test_run_local_accepts_relative_local_executable(monkeypatch, tmp_path):
@@ -168,7 +328,7 @@ def _fake_run(cmd, **kwargs):
 
     sim = DrivenSim()
     sim.set_output_dir(output_dir)
-    result = sim.run_local(num_processes=1, verbose=False)
+    result = sim.run_local(num_processes=1, verbose=False, use_apptainer=True)
 
     assert isinstance(result, dict)
     cmd = cast(list[str], captured["cmd"])
diff --git a/tests/palace/test_sim_classes.py b/tests/palace/test_sim_classes.py
index 850c5b6e..bddc6b05 100644
--- a/tests/palace/test_sim_classes.py
+++ b/tests/palace/test_sim_classes.py
@@ -246,8 +246,21 @@ def test_set_airbox(self):
                 "margin_y": 30.0,
                 "z_above": 100.0,
                 "z_below": 80.0,
+                "material": "air",
             }
 
+    def test_set_airbox_material(self):
+        """set_airbox(material=...) stores a custom background material."""
+        for cls in [DrivenSim, EigenmodeSim, ElectrostaticSim, BoundaryModeSim]:
+            sim = cls()
+            sim.set_airbox(material="sio2", margin_y=2.0)
+            assert sim._airbox_config["material"] == "sio2"
+            assert sim._airbox_config["margin_y"] == 2.0
+            with pytest.raises(ValueError, match="material"):
+                sim.set_airbox(material="")
+            with pytest.raises(ValueError, match="material"):
+                sim.set_airbox(material=123)  # ty: ignore[invalid-argument-type]
+
     def test_set_airbox_defaults_to_zero(self):
         """Unassigned set_airbox arguments should default to 0.0."""
         for cls in [DrivenSim, EigenmodeSim, ElectrostaticSim]:
@@ -258,6 +271,7 @@ def test_set_airbox_defaults_to_zero(self):
                 "margin_y": 0.0,
                 "z_above": 0.0,
                 "z_below": 0.0,
+                "material": "air",
             }
 
     def test_set_airbox_partial_defaults(self):
@@ -269,6 +283,7 @@ def test_set_airbox_partial_defaults(self):
             "margin_y": 0.0,
             "z_above": 0.0,
             "z_below": 0.0,
+            "material": "air",
         }
 
     def test_set_airbox_invalid(self):
@@ -279,7 +294,7 @@ def test_set_airbox_invalid(self):
 
     def test_mesh_routes_airbox_kwargs_through_set_airbox(self, monkeypatch, tmp_path):
         """mesh() air-region kwargs should be applied via set_airbox()."""
-        captured: dict[str, float | None] = {}
+        captured: dict[str, object] = {}
 
         def _fake_set_airbox(
             _self,
@@ -288,11 +303,13 @@ def _fake_set_airbox(
             margin_y=None,
             z_above=None,
             z_below=None,
+            material="air",
         ):
             captured["margin_x"] = margin_x
             captured["margin_y"] = margin_y
             captured["z_above"] = z_above
             captured["z_below"] = z_below
+            captured["material"] = material
 
         def _fake_generate_mesh_internal(_self, **_kwargs):
             return SimpleNamespace(mesh_stats={}, mesh_path=tmp_path / "palace.msh")
@@ -339,8 +356,50 @@ def _fake_validate_config(_self):
             "margin_y": 10.0,
             "z_above": 120.0,
             "z_below": 80.0,
+            "material": "air",
         }
 
+    def test_mesh_preserves_background_material(self, monkeypatch, tmp_path):
+        """mesh() margin overrides must not reset the background material to air."""
+        captured: dict[str, object] = {}
+
+        def _fake_set_airbox(_self, **kwargs):
+            captured.update(kwargs)
+
+        def _fake_generate_mesh_internal(_self, **_kwargs):
+            return SimpleNamespace(mesh_stats={}, mesh_path=tmp_path / "palace.msh")
+
+        sim = DrivenSim()
+        sim.set_output_dir(tmp_path / "sim")
+        sim.set_airbox(material="sio2", margin_y=3.0)
+
+        monkeypatch.setattr(DrivenSim, "set_airbox", _fake_set_airbox)
+        monkeypatch.setattr(
+            DrivenSim,
+            "validate_config",
+            lambda _self: SimpleNamespace(valid=True, errors=[]),
+        )
+        monkeypatch.setattr(DrivenSim, "_resolve_stack", lambda _self: object())
+        monkeypatch.setattr(
+            DrivenSim,
+            "_configure_ports_on_component",
+            lambda _self, _stack: None,
+        )
+        monkeypatch.setattr(
+            "gsim.palace.ports.extract_ports",
+            lambda _component, _stack: [],
+        )
+        monkeypatch.setattr(
+            DrivenSim,
+            "_generate_mesh_internal",
+            _fake_generate_mesh_internal,
+        )
+
+        sim.mesh(margin_y=50.0, verbose=False)
+
+        assert captured["material"] == "sio2"
+        assert captured["margin_y"] == 50.0
+
     def test_set_airbox_margin_y_zero_reaches_generate_mesh(
         self, monkeypatch, tmp_path
     ):
diff --git a/tests/test_viz_mesh.py b/tests/test_viz_mesh.py
index fdeded72..dc7e2bc3 100644
--- a/tests/test_viz_mesh.py
+++ b/tests/test_viz_mesh.py
@@ -4,6 +4,7 @@
 
 import sys
 from pathlib import Path
+from typing import Any, cast
 
 import meshio
 import numpy as np
@@ -209,3 +210,364 @@ def test_plot_solid_skips_unsupported_blocks(tmp_path: Path) -> None:
     viz.plot_mesh(msh, output=out, interactive=False, style="solid")
 
     assert out.exists()
+
+
+@_SKIP_RENDER_ON_WIN
+def test_plot_mesh_2d_camera_faces_plane(
+    tmp_path: Path, monkeypatch: pytest.MonkeyPatch
+) -> None:
+    """plot_mesh on a 2D mesh points the camera straight at the plane."""
+    msh = tmp_path / "flat.msh"
+    _write_minimal_msh(msh)
+
+    captured: dict[str, object] = {}
+
+    def _spy(plotter: Any, **_kwargs: object) -> None:
+        captured["camera"] = plotter.camera
+        plotter.close()
+
+    monkeypatch.setattr(viz, "_show_or_screenshot", _spy)
+
+    viz.plot_mesh(msh, interactive=True, mode="live")
+
+    camera: Any = captured["camera"]
+    view = np.array(camera.position) - np.array(camera.focal_point)
+    view /= np.linalg.norm(view)
+    # The fixture mesh is thin along z, so the camera must face +z/-z.
+    assert np.allclose(np.abs(view), [0.0, 0.0, 1.0])
+
+
+@_SKIP_RENDER_ON_WIN
+def test_plot_mesh_3d_keeps_iso_camera(
+    tmp_path: Path, monkeypatch: pytest.MonkeyPatch
+) -> None:
+    """plot_mesh on a 3D mesh keeps the default isometric view."""
+    msh = tmp_path / "vol.msh"
+    _write_minimal_msh(msh, use_3d=True)
+
+    captured: dict[str, object] = {}
+
+    def _spy(plotter: Any, **_kwargs: object) -> None:
+        captured["camera"] = plotter.camera
+        plotter.close()
+
+    monkeypatch.setattr(viz, "_show_or_screenshot", _spy)
+
+    viz.plot_mesh(msh, interactive=True, mode="live")
+
+    camera: Any = captured["camera"]
+    view = np.array(camera.position) - np.array(camera.focal_point)
+    view /= np.linalg.norm(view)
+    # Isometric view is not aligned to a single axis.
+    assert sum(abs(d) > 0.5 for d in view) > 1
+
+
+class _FakePlotter:
+    """Minimal stand-in for a PyVista plotter in mode-resolution tests."""
+
+    _id_counter = 0
+    camera_position = None
+
+    def __init__(self) -> None:
+        self.shown = 0
+        self.screenshotted = 0
+        self.closed = 0
+        self.notebook = False
+        self._id_name = f"fake-{_FakePlotter._id_counter}"
+        _FakePlotter._id_counter += 1
+
+    def show_axes(self) -> None:
+        return None
+
+    def render(self) -> None:
+        return None
+
+    def show(self, **_kwargs: object) -> _FakePlotter:
+        self.shown += 1
+        return self
+
+    def screenshot(self, _path: object) -> None:
+        self.screenshotted += 1
+
+    def close(self) -> None:
+        self.closed += 1
+
+
+def test_show_or_screenshot_static_when_interactive_off(
+    monkeypatch: pytest.MonkeyPatch,
+) -> None:
+    """With the session flag off, auto (interactive=None) renders a static PNG."""
+    viz._LIVE_PLOTTERS.clear()
+    monkeypatch.setattr(viz, "_INTERACTIVE_MODE", False)
+    monkeypatch.setattr(viz, "_in_notebook", lambda: False)
+
+    plotter = _FakePlotter()
+    viz._show_or_screenshot(plotter, interactive=None, mode="auto")
+    assert plotter.shown == 0
+    assert plotter.screenshotted == 1
+    assert viz._LIVE_PLOTTERS == {}
+
+
+def test_interactive_true_forces_live_even_when_off(
+    monkeypatch: pytest.MonkeyPatch,
+) -> None:
+    """interactive=True forces a live view even when the session flag is off."""
+    viz._LIVE_PLOTTERS.clear()
+    monkeypatch.setattr(viz, "_INTERACTIVE_MODE", False)
+    monkeypatch.setattr(viz, "_in_notebook", lambda: False)
+
+    plotter = _FakePlotter()
+    viz._show_or_screenshot(plotter, interactive=True, mode="auto")
+    assert plotter.shown == 1
+    assert plotter.screenshotted == 0
+    assert {plotter._id_name: plotter} == viz._LIVE_PLOTTERS
+
+
+def test_desktop_live_replaces_previous(monkeypatch: pytest.MonkeyPatch) -> None:
+    """Outside a notebook, a live plot replaces any previously open live view."""
+    viz._LIVE_PLOTTERS.clear()
+    monkeypatch.setattr(viz, "_INTERACTIVE_MODE", True)
+    monkeypatch.setattr(viz, "_in_notebook", lambda: False)
+
+    first = _FakePlotter()
+    viz._show_or_screenshot(first, interactive=True, mode="auto")
+    assert first.shown == 1
+    assert first.screenshotted == 0
+    assert {first._id_name: first} == viz._LIVE_PLOTTERS
+
+    second = _FakePlotter()
+    viz._show_or_screenshot(second, interactive=True, mode="auto")
+    assert second.shown == 1
+    assert first.closed == 1
+    assert {second._id_name: second} == viz._LIVE_PLOTTERS
+
+
+def test_notebook_keeps_multiple_views(monkeypatch: pytest.MonkeyPatch) -> None:
+    """In a notebook each interactive plot adds a widget to the shared trame server."""
+    viz._LIVE_PLOTTERS.clear()
+    monkeypatch.setattr(viz, "_INTERACTIVE_MODE", True)
+    monkeypatch.setattr(viz, "_in_notebook", lambda: True)
+
+    first = _FakePlotter()
+    first.notebook = True
+    viz._show_or_screenshot(first, interactive=True, mode="auto")
+    assert first.shown == 1
+    assert first.closed == 0
+
+    second = _FakePlotter()
+    second.notebook = True
+    viz._show_or_screenshot(second, interactive=True, mode="auto")
+    assert second.shown == 1
+    assert second.closed == 0
+    assert first.closed == 0  # previous view stays alive
+    assert len(viz._LIVE_PLOTTERS) == 2
+
+
+def test_notebook_uses_trame_backend_by_default(
+    monkeypatch: pytest.MonkeyPatch,
+) -> None:
+    """Notebook live views use server-side trame rendering by default."""
+    viz._LIVE_PLOTTERS.clear()
+    monkeypatch.setattr(viz, "_in_notebook", lambda: True)
+    monkeypatch.setattr(viz, "_TRAME_BACKEND", "trame")
+
+    seen: dict[str, object] = {}
+    plotter = _FakePlotter()
+    plotter.notebook = True
+
+    def _show(**_kwargs: object) -> _FakePlotter:
+        seen["backend"] = _kwargs.get("jupyter_backend")
+        return plotter
+
+    monkeypatch.setattr(plotter, "show", _show)
+
+    viz._show_or_screenshot(plotter, interactive=True, mode="live")
+    assert seen["backend"] == "trame"
+    assert {plotter._id_name: plotter} == viz._LIVE_PLOTTERS
+
+
+def test_notebook_live_view_silences_trame_debug_logs(
+    monkeypatch: pytest.MonkeyPatch,
+) -> None:
+    """Trame's template/state debug loggers are quiet while a live view is built.
+
+    The Vue-template tokenisation trame logs at INFO on every widget render
+    floods notebook consoles.  ``_show_live`` must raise those loggers to
+    WARNING for the duration of ``show()`` and restore them afterwards.
+    """
+    import logging
+
+    noisy = ("trame", "trame_client", "trame_server", "trame_vtk", "trame_vuetify")
+    for name in noisy:
+        logging.getLogger(name).setLevel(logging.NOTSET)
+    try:
+        viz._LIVE_PLOTTERS.clear()
+        monkeypatch.setattr(viz, "_in_notebook", lambda: True)
+        monkeypatch.setattr(viz, "_TRAME_BACKEND", "trame")
+
+        seen: dict[str, object] = {}
+        plotter = _FakePlotter()
+        plotter.notebook = True
+
+        def _show(**_kwargs: object) -> _FakePlotter:
+            seen["levels"] = {name: logging.getLogger(name).level for name in noisy}
+            return plotter
+
+        monkeypatch.setattr(plotter, "show", _show)
+
+        viz._show_or_screenshot(plotter, interactive=True, mode="live")
+
+        levels = cast(dict[str, int], seen["levels"])
+        for name, level in levels.items():
+            assert level >= logging.WARNING, f"{name} not silenced (level={level})"
+
+        # Levels restored after the live view is created.
+        for name in noisy:
+            assert logging.getLogger(name).level == logging.NOTSET
+        assert plotter._id_name in viz._LIVE_PLOTTERS
+    finally:
+        for name in noisy:
+            logging.getLogger(name).setLevel(logging.NOTSET)
+
+
+def test_set_trame_backend_validates() -> None:
+    """set_trame_backend accepts trame/client and rejects anything else."""
+    viz.set_trame_backend("client")
+    assert viz._TRAME_BACKEND == "client"
+    viz.set_trame_backend("trame")
+    assert viz._TRAME_BACKEND == "trame"
+    with pytest.raises(ValueError, match="backend"):
+        viz.set_trame_backend("bogus")  # ty: ignore[invalid-argument-type]
+
+
+def test_notebook_widget_failure_falls_back_to_static(
+    monkeypatch: pytest.MonkeyPatch,
+) -> None:
+    """If the interactive widget cannot be created, show a static image instead."""
+    viz._LIVE_PLOTTERS.clear()
+    monkeypatch.setattr(viz, "_INTERACTIVE_MODE", True)
+    monkeypatch.setattr(viz, "_in_notebook", lambda: True)
+
+    plotter = _FakePlotter()
+    plotter.notebook = True
+
+    def _broken_show(**_kwargs: object) -> None:
+        raise RuntimeError("trame widget failed")
+
+    monkeypatch.setattr(plotter, "show", _broken_show)
+
+    viz._show_or_screenshot(plotter, interactive=True, mode="auto")
+    assert plotter.shown == 0
+    assert plotter.screenshotted == 1
+    assert plotter.closed == 1
+    assert viz._LIVE_PLOTTERS == {}
+
+
+def test_mode_live_forces_show_desktop(monkeypatch: pytest.MonkeyPatch) -> None:
+    """mode='live' forces a live view, replacing any open view outside a notebook."""
+    viz._LIVE_PLOTTERS.clear()
+    monkeypatch.setattr(viz, "_INTERACTIVE_MODE", False)
+    monkeypatch.setattr(viz, "_in_notebook", lambda: False)
+
+    prev = _FakePlotter()
+    viz._LIVE_PLOTTERS[prev._id_name] = prev
+
+    forced = _FakePlotter()
+    viz._show_or_screenshot(forced, interactive=True, mode="live")
+    assert forced.shown == 1
+    assert prev.closed == 1
+
+
+def test_mode_static_always_screenshots(monkeypatch: pytest.MonkeyPatch) -> None:
+    """mode='static' renders a screenshot even before any live view."""
+    viz._LIVE_PLOTTERS.clear()
+    monkeypatch.setattr(viz, "_INTERACTIVE_MODE", True)
+
+    static = _FakePlotter()
+    viz._show_or_screenshot(static, interactive=True, mode="static")
+    assert static.shown == 0
+    assert static.screenshotted == 1
+    assert viz._LIVE_PLOTTERS == {}
+
+
+def test_interactive_false_screenshots_even_in_live_mode(
+    monkeypatch: pytest.MonkeyPatch,
+) -> None:
+    """interactive=False forces a static screenshot even when mode='live'."""
+    viz._LIVE_PLOTTERS.clear()
+    monkeypatch.setattr(viz, "_INTERACTIVE_MODE", True)
+    monkeypatch.setattr(viz, "_in_notebook", lambda: True)
+
+    plotter = _FakePlotter()
+    viz._show_or_screenshot(plotter, interactive=False, mode="live")
+    assert plotter.shown == 0
+    assert plotter.screenshotted == 1
+    assert viz._LIVE_PLOTTERS == {}
+
+
+def test_close_interactive_views() -> None:
+    """close_interactive_views closes every registered view and clears the registry."""
+    viz._LIVE_PLOTTERS.clear()
+    a, b = _FakePlotter(), _FakePlotter()
+    viz._LIVE_PLOTTERS[a._id_name] = a
+    viz._LIVE_PLOTTERS[b._id_name] = b
+
+    viz.close_interactive_views()
+    assert a.closed == 1
+    assert b.closed == 1
+    assert viz._LIVE_PLOTTERS == {}
+
+
+def test_close_interactive_view_single() -> None:
+    """close_interactive_view closes one registered view by id."""
+    viz._LIVE_PLOTTERS.clear()
+    a, b = _FakePlotter(), _FakePlotter()
+    viz._LIVE_PLOTTERS[a._id_name] = a
+    viz._LIVE_PLOTTERS[b._id_name] = b
+
+    viz.close_interactive_view(a._id_name)
+    assert a.closed == 1
+    assert b.closed == 0
+    assert a._id_name not in viz._LIVE_PLOTTERS
+
+
+def test_interactive_views_lists_ids() -> None:
+    """interactive_views returns the ids of all open views."""
+    viz._LIVE_PLOTTERS.clear()
+    a = _FakePlotter()
+    viz._LIVE_PLOTTERS[a._id_name] = a
+    assert viz.interactive_views() == (a._id_name,)
+
+
+def test_mode_for_respects_interactive_mode(monkeypatch: pytest.MonkeyPatch) -> None:
+    """auto is static by default and live only when interactive mode is enabled."""
+    monkeypatch.setattr(viz, "_VIZ_MODE", "auto")
+
+    monkeypatch.setattr(viz, "_INTERACTIVE_MODE", False)
+    assert viz._mode_for("auto") == "static"
+
+    monkeypatch.setattr(viz, "_INTERACTIVE_MODE", True)
+    assert viz._mode_for("auto") == "live"
+
+    monkeypatch.setattr(viz, "_VIZ_MODE", "static")
+    assert viz._mode_for("auto") == "static"
+
+    monkeypatch.setattr(viz, "_VIZ_MODE", "live")
+    assert viz._mode_for("auto") == "live"
+
+    monkeypatch.setattr(viz, "_VIZ_MODE", "auto")
+    monkeypatch.setattr(viz, "_INTERACTIVE_MODE", False)
+    assert viz._mode_for("auto") == "static"
+    assert viz._mode_for("live") == "live"
+    assert viz._mode_for("static") == "static"
+    monkeypatch.setattr(viz, "_INTERACTIVE_MODE", False)
+
+
+def test_set_interactive_mode_toggles_flag() -> None:
+    """The interactive mode flag is off by default and toggles via the setter."""
+    viz.set_interactive_mode(False)
+    assert viz.interactive_mode() is False
+    viz.set_interactive_mode(True)
+    assert viz.interactive_mode() is True
+    viz.set_interactive_mode(False)
+    assert viz.interactive_mode() is False