{
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"source": [
"# Coaxial cable mesh"
]
},
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"source": [
"from palacetoolkit.viz import view_mesh\n",
"from palacetoolkit.geometry import extract_tag, xmin, xmax, ymin, ymax, zmin, zmax\n",
"import math\n",
"import gmsh\n",
"\n"
]
},
{
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"Parameters:\n",
"\n",
"- filename - the filename to use for the generated mesh.\n",
"- refinement - measure of how many elements to include, 0 is least\n",
"- order - the polynomial order of the approximation, minimum 1\n",
"- inner_diameter_mm - the inner diameter of the cable, in millimeters\n",
"- outer_diameter_mm - the outer diameter of the cable, in millimeters\n",
"- length_mm - the length of the cable, in millimeters\n",
"- verbose - flag to dictate the level of print to REPL, passed to Gmsh\n",
"- gui - whether to launch the Gmsh GUI on mesh generation"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "88f3a33d",
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"source": [
"filename : str = \"coax.msh\" \n",
"refinement : int = 2 \n",
"order : int = 2 \n",
"inner_diameter_mm : float = 1.6383 \n",
"outer_diameter_mm : float = 5.461 \n",
"length_mm : float = 40.0\n",
"verbose : int = 5\n",
"gui : bool = True "
]
},
{
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"id": "74ea6cc0",
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"tags": []
},
"source": [
"Check that the geometry makes sense."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "f1f466d5",
"metadata": {
"execution": {
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"source": [
"assert outer_diameter_mm > inner_diameter_mm > 0\n",
"assert length_mm > 0\n",
"assert refinement >= 0\n",
"assert order > 0 "
]
},
{
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"id": "406b0c2f",
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"source": [
"## Initialization of the model."
]
},
{
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"source": [
"# Creates a reference to the geometry module based on OpenCASCADE (OCC).\n",
"kernel = gmsh.model.occ\n",
"\n",
"# Initialize gmsh.\n",
"gmsh.initialize()\n",
"\n",
"# Set the verbosity of the output.\n",
"gmsh.option.setNumber(\"General.Verbosity\", verbose)"
]
},
{
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"id": "f5c72ae7",
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"tags": []
},
"source": [
"## Geometry definitions."
]
},
{
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"source": [
"# Geometry (en mm)\n",
"inner_radio = inner_diameter_mm / 2\n",
"outer_radio = outer_diameter_mm / 2\n",
"\n",
"# Mesh parameters\n",
"n_circum = 4 * 2**refinement \n",
"n_length = 4 * 2**refinement\n",
" \n",
"# Geometry\n",
"p0 = kernel.addPoint(inner_radio, 0, 0)\n",
"p1 = kernel.addPoint(outer_radio, 0, 0)\n",
"\n",
"l0 = kernel.addLine(p0, p1)"
]
},
{
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"source": [
"## Revolve operation - base face generation.\n",
"\n",
"Rotate the line (l_0) around the z-axis.\n",
"\n",
"- First revolve (base_face_0) is made with a 180° degree and n_circum//2 divisions.\n",
"- Seconde revolve (base_face_1) with a -180° degree and n_circum//2 divisions."
]
},
{
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"execution_count": 6,
"id": "8f7c9081",
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"source": [
"base_face_0 = kernel.revolve(\n",
" [(1, l0)], # list of entities to rotate (dim=1 → curve, tag=l0)\n",
" 0.0, 0.0, 0.0, # origin point of rotation\n",
" 0.0, 0.0, 1.0, # rotation axis (here, the z-axis)\n",
" math.pi, # rotation angle (180°)\n",
" [n_circum // 2], # number of divisions in the angular direction\n",
" [1.0], # scale factor for the mesh size (1.0 means no scaling)\n",
" recombine=True # recombinar las caras resultantes\n",
" )\n",
" \n",
"base_face_1 = kernel.revolve(\n",
" [(1, l0)], \n",
" 0.0, 0.0, 0.0, \n",
" 0.0, 0.0, 1.0, \n",
" -math.pi, \n",
" [n_circum//2], \n",
" [1.0], \n",
" recombine=True \n",
")"
]
},
{
"cell_type": "markdown",
"id": "79879482",
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"source": [
"kernel.revolve returns a list of entities created by the revolution, each one represented as a tuple (dim, tag).\n",
"- dim is the dimension of the entity (0 for points, 1 for lines, 2 for surfaces, 3 for volumes).\n",
"- A tag is a unique identifier assigned by Gmsh to each entity created.\n",
"\n",
"We will filter these lists to keep only the surfaces (dim=2) that represent the cylinder faces, \n",
"discarding any other entities that may have been created during the revolution.\n",
"\n",
"In this case the revolution returns [(1, 4), (2, 1), (1, 2), (1, 3)]. We are only interested in\n",
"(2, 1), which is the surface created by the revolution, and we discard the lines (1, 4), (1, 2), (1, 3)."
]
},
{
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"execution_count": 7,
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"source": [
"base_face_0 = [x for x in base_face_0 if x[0] == 2]\n",
"base_face_1 = [x for x in base_face_1 if x[0] == 2]\n",
"\n",
"# Check that there was generated only one face.\n",
"assert len(base_face_0) == 1 and len(base_face_1) == 1"
]
},
{
"cell_type": "markdown",
"id": "587441fd",
"metadata": {
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},
"source": [
"Now, we extrude the base faces to get the cylinder."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "d4d8c594",
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"source": [
"# Extrude the faces along the z-axis. \n",
"cylinder_0 = kernel.extrude(\n",
" base_face_0, # List of entities (dim=2, tag)\n",
" 0.0, 0.0, length_mm, # How much extrusion in (x, y, z)\n",
" [n_length], # Divisions in the direction of the extrusion\n",
" [1.0], # Scale\n",
" recombine=True # recombine faces\n",
")\n",
"\n",
"cylinder_1 = kernel.extrude(\n",
" base_face_1,\n",
" 0.0, 0.0, length_mm,\n",
" [n_length],\n",
" [1.0],\n",
" recombine=True\n",
")"
]
},
{
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"source": [
"\n",
"We keep only the tags of the faces and volumes created by the extrusion, filtering by dimension.\n",
"Remember that cylinder_0 and cylinder_1 are lists of tuples (dim, tag) representing all \n",
"entities created by the extrusion, including lines, surfaces, and volumes. We are interested \n",
"only in the faces (dim=2) that form the cylinder end caps, and in the volumes (dim=3) \n",
"that represent the cylinder body.\n"
]
},
{
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"source": [
"base_face_0 = base_face_0[0][1] # Tag of the first surface.\n",
"base_face_1 = base_face_1[0][1] \n",
"\n",
"far_face_0 = cylinder_0[0][1] \n",
"cylinder_0 = cylinder_0[1][1] \n",
"\n",
"far_face_1 = cylinder_1[0][1]\n",
"cylinder_1 = cylinder_1[1][1]"
]
},
{
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},
"source": [
"Fragment the geometry to create a valid mesh. This is necessary because we have extruded two faces that share an edge, and we need to ensure that the resulting geometry is properly connected. "
]
},
{
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{
"name": "stdout",
"output_type": "stream",
"text": [
"Info : Rebinding OpenCASCADE point 3 \n",
"Info : Rebinding OpenCASCADE point 4\n",
"Info : Cannot bind existing OpenCASCADE point 3 to second tag 5\n",
"Info : Could not preserve tag of 0D object 5 (->3)\n",
"Info : Cannot bind existing OpenCASCADE point 4 to second tag 6\n",
"Info : Could not preserve tag of 0D object 6 (->4)\n",
"Info : Rebinding OpenCASCADE point 7\n",
"Info : Rebinding OpenCASCADE point 8\n",
"Info : Rebinding OpenCASCADE point 9\n",
"Info : Rebinding OpenCASCADE point 10\n",
"Info : Cannot bind existing OpenCASCADE point 7 to second tag 11\n",
"Info : Could not preserve tag of 0D object 11 (->7)\n",
"Info : Cannot bind existing OpenCASCADE point 8 to second tag 12\n",
"Info : Could not preserve tag of 0D object 12 (->8)\n",
"Info : Cannot bind existing OpenCASCADE point 9 to second tag 13\n",
"Info : Could not preserve tag of 0D object 13 (->9)\n",
"Info : Cannot bind existing OpenCASCADE point 10 to second tag 14\n",
"Info : Could not preserve tag of 0D object 14 (->10)\n",
"Info : Rebinding OpenCASCADE curve 2\n",
"Info : Rebinding OpenCASCADE curve 3\n",
"Info : Rebinding OpenCASCADE curve 4\n",
"Info : Rebinding OpenCASCADE curve 5\n",
"Info : Rebinding OpenCASCADE curve 6\n",
"Info : Cannot bind existing OpenCASCADE curve 4 to second tag 7\n",
"Info : Could not preserve tag of 1D object 7 (->4)\n",
"Info : Rebinding OpenCASCADE curve 8\n",
"Info : Rebinding OpenCASCADE curve 9\n",
"Info : Rebinding OpenCASCADE curve 10\n",
"Info : Rebinding OpenCASCADE curve 11\n",
"Info : Rebinding OpenCASCADE curve 12\n",
"Info : Rebinding OpenCASCADE curve 13\n",
"Info : Rebinding OpenCASCADE curve 14\n",
"Info : Rebinding OpenCASCADE curve 15\n",
"Info : Cannot bind existing OpenCASCADE curve 8 to second tag 16\n",
"Info : Could not preserve tag of 1D object 16 (->8)\n",
"Info : Cannot bind existing OpenCASCADE curve 9 to second tag 17\n",
"Info : Could not preserve tag of 1D object 17 (->9)\n",
"Info : Rebinding OpenCASCADE curve 18\n",
"Info : Cannot bind existing OpenCASCADE curve 11 to second tag 19\n",
"Info : Could not preserve tag of 1D object 19 (->11)\n",
"Info : Cannot bind existing OpenCASCADE curve 12 to second tag 20\n",
"Info : Could not preserve tag of 1D object 20 (->12)\n",
"Info : Rebinding OpenCASCADE curve 21\n",
"Info : Cannot bind existing OpenCASCADE curve 14 to second tag 22\n",
"Info : Could not preserve tag of 1D object 22 (->14)\n",
"Info : Cannot bind existing OpenCASCADE curve 15 to second tag 23\n",
"Info : Could not preserve tag of 1D object 23 (->15)\n",
"Info : Rebinding OpenCASCADE surface 1\n",
"Info : Rebinding OpenCASCADE surface 2\n",
"Info : Rebinding OpenCASCADE surface 3\n",
"Info : Rebinding OpenCASCADE surface 4\n",
"Info : Rebinding OpenCASCADE surface 5\n",
"Info : Rebinding OpenCASCADE surface 6\n",
"Info : Rebinding OpenCASCADE surface 7\n",
"Info : Rebinding OpenCASCADE surface 8\n",
"Info : Rebinding OpenCASCADE surface 9\n",
"Info : Cannot bind existing OpenCASCADE surface 5 to second tag 10\n",
"Info : Could not preserve tag of 2D object 10 (->5)\n",
"Info : Cannot bind existing OpenCASCADE surface 6 to second tag 11\n",
"Info : Could not preserve tag of 2D object 11 (->6)\n",
"Info : Rebinding OpenCASCADE surface 12\n"
]
}
],
"source": [
"# Remove duplicates (if there is any) and preserve the original geometry.\n",
"kernel.fragment(kernel.getEntities(), [])\n",
"kernel.synchronize()"
]
},
{
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"source": [
"# Get the boundaries deleting non necessary surfaces\n",
"boundaries = []\n",
"for cylinder in [cylinder_0, cylinder_1]:\n",
" _, local_boundaries = gmsh.model.getAdjacencies(3, cylinder)\n",
" local_delete = []\n",
" for boundary in local_boundaries:\n",
" if boundary not in boundaries:\n",
" boundaries.append(boundary)\n",
" else:\n",
" local_delete.append(boundaries.index(boundary))\n",
" # eliminar duplicados\n",
" for idx in sorted(local_delete, reverse=True):\n",
" del boundaries[idx]\n",
"\n",
"# Delete faces\n",
"for face in [base_face_0, base_face_1, far_face_0, far_face_1]:\n",
" if face in boundaries:\n",
" boundaries.remove(face)"
]
},
{
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"id": "84119459",
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},
"source": [
"## Defining the Physical groups."
]
},
{
"cell_type": "code",
"execution_count": 12,
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"cylinder_group = gmsh.model.addPhysicalGroup(3, [cylinder_0, cylinder_1], -1, \"cylinder\") \n",
"boundary_group = gmsh.model.addPhysicalGroup(2, boundaries, -1, \"boundaries\") \n",
"port1_group = gmsh.model.addPhysicalGroup(2, [base_face_0, base_face_1], -1, \"port1\") \n",
"port2_group = gmsh.model.addPhysicalGroup(2, [far_face_0, far_face_1], -1, \"port2\")"
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"source": [
"## Mesh settings and generation."
]
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"Info : Meshing 1D...\n",
"Info : [ 0%] Meshing curve 1 (Line)\n",
"Info : [ 10%] Meshing curve 2 (Extruded)\n",
"Info : [ 20%] Meshing curve 3 (Extruded)\n",
"Info : [ 20%] Meshing curve 4 (Extruded)\n",
"Info : [ 30%] Meshing curve 5 (Extruded)\n",
"Info : [ 40%] Meshing curve 6 (Extruded)\n",
"Info : [ 40%] Meshing curve 8 (Extruded)\n",
"Info : [ 50%] Meshing curve 9 (Extruded)\n",
"Info : [ 60%] Meshing curve 10 (Extruded)\n",
"Info : [ 60%] Meshing curve 11 (Extruded)\n",
"Info : [ 70%] Meshing curve 12 (Extruded)\n",
"Info : [ 70%] Meshing curve 13 (Extruded)\n",
"Info : [ 80%] Meshing curve 14 (Extruded)\n",
"Info : [ 90%] Meshing curve 15 (Extruded)\n",
"Info : [ 90%] Meshing curve 18 (Extruded)\n",
"Info : [100%] Meshing curve 21 (Extruded)\n",
"Info : Done meshing 1D (Wall 0.000124882s, CPU 0.000294s)\n",
"Info : Meshing 2D...\n",
"Info : [ 0%] Meshing surface 1 (Extruded)\n",
"Info : [ 20%] Meshing surface 2 (Extruded)\n",
"Info : [ 30%] Meshing surface 3 (Extruded)\n",
"Info : [ 40%] Meshing surface 4 (Extruded)\n",
"Info : [ 50%] Meshing surface 5 (Extruded)\n",
"Info : [ 60%] Meshing surface 6 (Extruded)\n",
"Info : [ 70%] Meshing surface 7 (Extruded)\n",
"Info : [ 80%] Meshing surface 8 (Extruded)\n",
"Info : [ 90%] Meshing surface 9 (Extruded)\n",
"Info : [100%] Meshing surface 12 (Extruded)\n",
"Info : Done meshing 2D (Wall 0.00464383s, CPU 0.00181s)\n",
"Info : Meshing 3D...\n",
"Info : Meshing volume 1 (Extruded)\n",
"Info : Meshing volume 2 (Extruded)\n",
"Info : Done meshing 3D (Wall 0.000631244s, CPU 0.000508s)\n",
"Info : Optimizing mesh...\n",
"Info : Done optimizing mesh (Wall 6.853e-06s, CPU 0s)\n",
"Info : 544 nodes 972 elements\n",
"Info : Meshing order 2 (curvilinear on)...\n",
"Info : [ 0%] Meshing curve 1 order 2\n",
"Info : [ 10%] Meshing curve 2 order 2\n",
"Info : [ 10%] Meshing curve 3 order 2\n",
"Info : [ 20%] Meshing curve 4 order 2\n",
"Info : [ 20%] Meshing curve 5 order 2\n",
"Info : [ 20%] Meshing curve 6 order 2\n",
"Info : [ 30%] Meshing curve 8 order 2\n",
"Info : [ 30%] Meshing curve 9 order 2\n",
"Info : [ 30%] Meshing curve 10 order 2\n",
"Info : [ 40%] Meshing curve 11 order 2\n",
"Info : [ 40%] Meshing curve 12 order 2\n",
"Info : [ 40%] Meshing curve 13 order 2\n",
"Info : [ 50%] Meshing curve 14 order 2\n",
"Info : [ 50%] Meshing curve 15 order 2\n",
"Info : [ 60%] Meshing curve 18 order 2\n",
"Info : [ 60%] Meshing curve 21 order 2\n",
"Info : [ 60%] Meshing surface 1 order 2\n",
"Info : [ 70%] Meshing surface 2 order 2\n",
"Info : [ 70%] Meshing surface 3 order 2\n",
"Info : [ 70%] Meshing surface 4 order 2\n",
"Info : [ 80%] Meshing surface 5 order 2\n",
"Info : [ 80%] Meshing surface 6 order 2\n",
"Info : [ 80%] Meshing surface 7 order 2\n",
"Info : [ 90%] Meshing surface 8 order 2\n",
"Info : [ 90%] Meshing surface 9 order 2\n",
"Info : [ 90%] Meshing surface 12 order 2\n",
"Info : [100%] Meshing volume 1 order 2\n",
"Info : [100%] Meshing volume 2 order 2\n",
"Info : Done meshing order 2 (Wall 0.00397241s, CPU 0.003217s)\n",
"Info : Writing 'coax.msh'...\n",
"\n",
"Finished generating mesh. Physical group tags:\n",
"Cylinder: 1\n",
"Boundaries: 2\n",
"Port 1: 3\n",
"Port 2: 4\n",
"\n",
"Info : Done writing 'coax.msh'\n",
"Loading mesh file: coax.msh\n",
"Groups to render transparent: ['air_none', 'air_plastic_enclosure']\n",
"\n",
"Mesh loaded successfully with 2 cell blocks\n",
"Found 1088 triangles total\n",
"Physical group tags in mesh: {2: 'boundaries', 3: 'port1', 4: 'port2'}\n"
]
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"def _generate_coax_mesh():\n",
" # Mesh options\n",
" gmsh.option.setNumber(\"Mesh.MinimumCurveNodes\", 2)\n",
" gmsh.option.setNumber(\"Mesh.MinimumCircleNodes\", 0)\n",
" gmsh.option.setNumber(\"Mesh.MeshSizeFromPoints\", 0)\n",
" gmsh.option.setNumber(\"Mesh.MeshSizeFromCurvature\", 0)\n",
" gmsh.option.setNumber(\"Mesh.MeshSizeExtendFromBoundary\", 0)\n",
"\n",
" # Set mesh algorithms\n",
" gmsh.option.setNumber(\"Mesh.Algorithm\", 6) # frontal (2D)\n",
" gmsh.option.setNumber(\"Mesh.Algorithm3D\", 1) # Delaunay (3D)\n",
"\n",
" # Generate 3D mesh\n",
" gmsh.model.mesh.generate(3)\n",
"\n",
" # Order of the mesh elements (1 = linear, 2 = quadratic)\n",
" gmsh.model.mesh.setOrder(order)\n",
"\n",
" # Save mesh\n",
" gmsh.option.setNumber(\"Mesh.MshFileVersion\", 2.2)\n",
" gmsh.option.setNumber(\"Mesh.Binary\", 1)\n",
" gmsh.write(filename)\n",
"\n",
" if verbose > 0:\n",
" print(\"\\nFinished generating mesh. Physical group tags:\")\n",
" print(\"Cylinder:\", cylinder_group)\n",
" print(\"Boundaries:\", boundary_group)\n",
" print(\"Port 1:\", port1_group)\n",
" print(\"Port 2:\", port2_group)\n",
" print()\n",
"\n",
"_generate_coax_mesh()\n",
"\n",
"gmsh.finalize()\n",
"view_mesh(filename)"
]
}
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