fix: merge same-material dielectric boxes and align XY extents

Adjacent dielectric boxes of the same material are now merged into a
single GMSH box (e.g. box+clad SiO2 → one volume), eliminating
coincident faces and sliver tets. Different-material boxes sharing a
z-boundary use removeAllDuplicates() to cleanly resolve the shared face.

Also adds a regression test verifying box/clad XY consistency, improves
the mesh summary in notebooks, and removes the plot_mesh_slice feature.

Author: vvahidd

nbs/mesh_ybranch.ipynb

@@ -37,6 +37,8 @@
     "# c = cells.ring_single()\n",
     "c = cells.coupler()\n",
     "\n",
+    "dirname = \"./sim-data-mesh-----coupler\"\n",
+    "\n",
     "c"
    ]
   },
@@ -106,7 +108,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "result = sim.mesh(\"./mesh-ybranch\")\n",
+    "result = sim.mesh(dirname, refined_mesh_size=0.2, max_mesh_size=1.0)\n",
     "config_path = sim.write_config()\n",
     "\n",
     "print(f\"Mesh file: {result.mesh_path}\")\n",
@@ -119,7 +121,7 @@
    "id": "7",
    "metadata": {},
    "source": [
-    "### Inspect mesh statistics"
+    "### Mesh summary"
    ]
   },
   {
@@ -129,62 +131,92 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "import json\n",
+    "import meshio\n",
+    "import numpy as np\n",
     "\n",
-    "# Mesh statistics\n",
     "stats = result.mesh_stats\n",
-    "print(\"=== Mesh Stats ===\")\n",
-    "print(json.dumps(stats, indent=2))\n",
-    "\n",
-    "# Config contents\n",
-    "print(\"\\n=== mesh_config.json ===\")\n",
-    "print(config_path.read_text())"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9",
-   "metadata": {},
-   "source": [
-    "### Inspect physical groups"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "10",
-   "metadata": {},
-   "outputs": [],
-   "source": [
     "groups = result.groups\n",
+    "m = meshio.read(result.mesh_path)\n",
+    "tag_to_name = {tag: name for name, (tag, _) in m.field_data.items()}\n",
     "\n",
-    "print(\"Volume groups (materials):\")\n",
-    "for name, info in groups[\"volumes\"].items():\n",
-    "    print(f\"  {name}: phys_group={info['phys_group']}, tags={info['tags']}\")\n",
+    "# --- Header ---\n",
+    "size_kb = result.mesh_path.stat().st_size / 1024\n",
+    "print(f\"Mesh: {result.mesh_path.name}  ({size_kb:.0f} KB)\")\n",
+    "print(f\"Nodes: {stats.get('nodes', '?'):,}   Tets: {stats.get('tetrahedra', '?'):,}\")\n",
+    "print()\n",
     "\n",
-    "print(\"\\nLayer volumes:\")\n",
-    "for name, info in groups[\"layer_volumes\"].items():\n",
-    "    print(\n",
-    "        f\"  {name}: phys_group={info['phys_group']}, material={info['material']}, tags={info['tags']}\"\n",
-    "    )\n",
+    "# --- Quality ---\n",
+    "q = stats.get(\"quality\", {})\n",
+    "sicn = stats.get(\"sicn\", {})\n",
+    "edge = stats.get(\"edge_length\", {})\n",
+    "print(\"Quality\")\n",
+    "print(\n",
+    "    f\"  Shape (gamma):  min={q.get('min', '?')}  mean={q.get('mean', '?')}  max={q.get('max', '?')}\"\n",
+    ")\n",
+    "print(\n",
+    "    f\"  SICN:           min={sicn.get('min', '?')}  mean={sicn.get('mean', '?')}  invalid={sicn.get('invalid', '?')}\"\n",
+    ")\n",
+    "print(f\"  Edge length:    min={edge.get('min', '?')}  max={edge.get('max', '?')}\")\n",
     "\n",
-    "if groups.get(\"port_surfaces\"):\n",
-    "    print(\"\\nPort surfaces:\")\n",
-    "    for name, info in groups[\"port_surfaces\"].items():\n",
+    "# Edge ratio from actual mesh\n",
+    "for cells in m.cells:\n",
+    "    if cells.type == \"tetra\":\n",
+    "        pts = m.points[cells.data]\n",
+    "        pairs = [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]\n",
+    "        all_edges = np.stack(\n",
+    "            [np.linalg.norm(pts[:, i] - pts[:, j], axis=1) for i, j in pairs]\n",
+    "        )\n",
+    "        ratios = all_edges.max(axis=0) / np.maximum(all_edges.min(axis=0), 1e-15)\n",
+    "        bad = int(np.sum(ratios > 20))\n",
     "        print(\n",
-    "            f\"  {name}: phys_group={info['phys_group']}, center={info['center']}, \"\n",
-    "            f\"width={info['width']}, layer={info['layer']}, z_range={info['z_range']}\"\n",
+    "            f\"  Edge ratio:     mean={ratios.mean():.1f}  max={ratios.max():.1f}  bad(>20)={bad}\"\n",
     "        )\n",
+    "print()\n",
+    "\n",
+    "# --- Bounding box ---\n",
+    "bb = stats.get(\"bbox\", {})\n",
+    "print(f\"Bounding box\")\n",
+    "print(\n",
+    "    f\"  x: [{bb.get('xmin', 0):.2f}, {bb.get('xmax', 0):.2f}]  ({bb.get('xmax', 0) - bb.get('xmin', 0):.2f} um)\"\n",
+    ")\n",
+    "print(\n",
+    "    f\"  y: [{bb.get('ymin', 0):.2f}, {bb.get('ymax', 0):.2f}]  ({bb.get('ymax', 0) - bb.get('ymin', 0):.2f} um)\"\n",
+    ")\n",
+    "print(\n",
+    "    f\"  z: [{bb.get('zmin', 0):.2f}, {bb.get('zmax', 0):.2f}]  ({bb.get('zmax', 0) - bb.get('zmin', 0):.2f} um)\"\n",
+    ")\n",
+    "print()\n",
     "\n",
-    "if groups.get(\"outer_boundary\"):\n",
-    "    print(f\"\\nOuter boundary: phys_group={groups['outer_boundary']['phys_group']}\")\n",
-    "else:\n",
-    "    print(\"\\nNo outer boundary (airbox not included)\")"
+    "# --- Physical groups ---\n",
+    "print(\"Physical groups\")\n",
+    "for cells, phys in zip(m.cells, m.cell_data[\"gmsh:physical\"]):\n",
+    "    if cells.type != \"tetra\":\n",
+    "        continue\n",
+    "    for tag, name in sorted(tag_to_name.items(), key=lambda x: x[1]):\n",
+    "        mask = phys == tag\n",
+    "        n = int(np.sum(mask))\n",
+    "        if n == 0:\n",
+    "            continue\n",
+    "        pts = m.points[cells.data[mask].ravel()]\n",
+    "        zlo, zhi = pts[:, 2].min(), pts[:, 2].max()\n",
+    "        mat = \"\"\n",
+    "        if name in groups.get(\"layer_volumes\", {}):\n",
+    "            mat = f\"  (material: {groups['layer_volumes'][name].get('material', '?')})\"\n",
+    "        print(f\"  {name:16s}  {n:>7,} tets   z=[{zlo:.3f}, {zhi:.3f}]{mat}\")\n",
+    "\n",
+    "if groups.get(\"port_surfaces\"):\n",
+    "    print()\n",
+    "    print(\"Port surfaces\")\n",
+    "    for name, info in groups[\"port_surfaces\"].items():\n",
+    "        c = info[\"center\"]\n",
+    "        print(\n",
+    "            f\"  {name:16s}  center=({c[0]:.2f}, {c[1]:.2f})  width={info['width']:.2f}  z=[{info['z_range'][0]:.3f}, {info['z_range'][1]:.3f}]\"\n",
+    "        )"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "11",
+   "id": "9",
    "metadata": {},
    "source": [
     "### Visualize the mesh"
@@ -193,18 +225,18 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "12",
+   "id": "10",
    "metadata": {},
    "outputs": [],
    "source": [
     "# Full mesh wireframe\n",
-    "sim.plot_mesh(interactive=False)"
+    "sim.plot_mesh(interactive=True)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "13",
+   "id": "11",
    "metadata": {},
    "outputs": [],
    "source": [