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"source": [
"### Open ended stub antenna\n",
"\n",
"An open-ended stub antenna is a simple radiating element consisting of a transmission line (typically microstrip or coaxial cable) with one end open-circuited, allowing electromagnetic energy to radiate directly into free space."
]
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"source": [
"import gmsh\n",
"import math\n",
"\n",
"from palacetoolkit.viz import view_mesh\n",
"from palacetoolkit.mesh import (\n",
" Entity, \n",
" run_meshing_pipeline, \n",
" generate_3d_mesh, \n",
" refine_near_surfaces\n",
")\n",
"from palacetoolkit.simulation import Simulation"
]
},
{
"cell_type": "markdown",
"id": "06f22ba1",
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"source": [
"### Paramters\n",
"- l1 : Ground plane length along x-axis, specified as a scalar in meters\n",
"- w1 : Ground plane width along y-axis, specified as a scalar in meters\n",
"- h : Patch height along z-axis, specified as a scalar in meters.\n",
"\n",
"- strip_line_length : Notch length along x-axis, specified as a scalar in meters. \n",
"- strip_lined_width: Notch width along y-axis, specified as a scalar in meters.\n",
"- air_height : Air-domain height reference for sizing the enclosing sphere, specified as a scalar in meters.\n",
"- air_margin : Air-domain margin along x and y axes used for sphere sizing, specified as a scalar in meters.\n",
"- freq : Simulation frequency in GHz, specified as a scalar.\n",
"- filename : Output mesh filename, specified as a string."
]
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{
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"execution_count": 2,
"id": "d854dab2",
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"source": [
"l1: float = 0.06\n",
"w1: float = 0.06\n",
"strip_line_length: float = 0.04\n",
"strip_line_width: float = 0.002\n",
"h: float = 0.0013\n",
"air_height: float = 0.025 \n",
"air_margin: float = 0.025 \n",
"freq: float = 3.3\n",
"filename: str = \"open_ended_antenna.msh\"\n",
"\n",
"wavelength = 3e8 / (freq * 1e9)"
]
},
{
"cell_type": "markdown",
"id": "20118c72",
"metadata": {
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"tags": []
},
"source": [
"### Model initialization"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "12cc3554",
"metadata": {
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"source": [
"gmsh.initialize()\n",
"gmsh.model.add(\"patch_antenna\")\n",
"kernel = gmsh.model.occ"
]
},
{
"cell_type": "markdown",
"id": "a4fbf049",
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"tags": []
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"source": [
"### Geometry construction"
]
},
{
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"source": [
"# Total domain bounds\n",
"total_xmin = -l1/2 - air_margin\n",
"total_xmax = l1/2 + air_margin\n",
"total_ymin = -w1/2 - air_margin\n",
"total_ymax = w1/2 + air_margin\n",
"total_zmax = h + air_height\n",
"\n",
"# Substrate box\n",
"substrate = kernel.addBox(-l1/2, -w1/2, 0, l1, w1, h)\n",
"\n",
"# Ground plane\n",
"ground_plane = kernel.addRectangle(-l1/2, -w1/2, 0, l1, w1)\n",
"\n",
"# Top conductor\n",
"strip_line_1 = kernel.addRectangle(-l1/2, -strip_line_width/2, h, strip_line_length, strip_line_width)\n",
"\n",
"# gap bewteen the ground plane and the bottom of the lumped port.\n",
"gap = 0\n",
"\n",
"# lumped port\n",
"lumped_port = kernel.addRectangle(-l1/2 + gap, -strip_line_width/2, 0, h - gap, strip_line_width)\n",
"kernel.rotate([(2, lumped_port)], -l1/2, 0, 0, 0, 1, 0, -math.pi/2)\n",
"\n",
"# Air sphere\n",
"airsphere_radius = max(abs(total_xmin), abs(total_xmax), abs(total_ymin), abs(total_ymax), total_zmax)\n",
"air_sphere = kernel.addSphere(0.0, 0.0, 0.0, airsphere_radius)\n",
"\n",
"# Synchronize everything!\n",
"kernel.synchronize()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "e4112dbf",
"metadata": {
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},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Physical group 'air_sphere' (dim=3): pg=1, tags=[2] \n",
" Physical group 'substrate' (dim=3): pg=2, tags=[1]\n",
" Physical group 'top_conductor' (dim=2): pg=3, tags=[8]\n",
" Physical group 'ground_plane' (dim=2): pg=4, tags=[7]\n",
" Physical group 'lumped_port' (dim=2): pg=5, tags=[9]\n",
" Physical group 'air_sphere__None' (dim=2): pg=6, tags=[16]\n",
" Physical group 'air_sphere__substrate' (dim=2): pg=7, tags=[10, 11, 13, 15, 14, 12]\n",
" ppw_near=50 ppw_far=30\n",
" SizeMax=0.0030 transition=0.0227\n",
" global: 4 curves, SizeMin=0.0018\n",
" local (2, 9): 4 curves, SizeMin=0.0006\n",
" Merged 2 fields with Min → field 5\n",
"Info : Meshing 1D...\n",
"Info : [ 0%] Meshing curve 24 (Line)\n",
"Info : [ 10%] Meshing curve 25 (Line)\n",
"Info : [ 10%] Meshing curve 26 (Line)\n",
"Info : [ 20%] Meshing curve 27 (Line)\n",
"Info : [ 20%] Meshing curve 28 (Line)\n",
"Info : [ 30%] Meshing curve 29 (Line)\n",
"Info : [ 30%] Meshing curve 30 (Line)\n",
"Info : [ 30%] Meshing curve 31 (Line)\n",
"Info : [ 40%] Meshing curve 32 (Line)\n",
"Info : [ 40%] Meshing curve 33 (Line)\n",
"Info : [ 50%] Meshing curve 34 (Line)\n",
"Info : [ 50%] Meshing curve 35 (Line)\n",
"Info : [ 60%] Meshing curve 36 (Line)\n",
"Info : [ 60%] Meshing curve 37 (Line)\n",
"Info : [ 60%] Meshing curve 38 (Line)\n",
"Info : [ 70%] Meshing curve 39 (Line)\n",
"Info : [ 70%] Meshing curve 40 (Line)\n",
"Info : [ 80%] Meshing curve 41 (Line)\n",
"Info : [ 80%] Meshing curve 42 (Line)\n",
"Info : [ 80%] Meshing curve 43 (Line)\n",
"Info : [ 90%] Meshing curve 45 (Circle)\n",
"Info : [100%] Meshing curve 47 (Line)\n",
"Info : Done meshing 1D (Wall 0.0227882s, CPU 0.023435s)\n",
"Info : Meshing 2D...\n",
"Info : [ 0%] Meshing surface 7 (Plane, MeshAdapt)\n",
"Info : [ 20%] Meshing surface 8 (Plane, MeshAdapt)\n",
"Info : [ 30%] Meshing surface 9 (Plane, MeshAdapt)\n",
"Info : [ 40%] Meshing surface 10 (Plane, MeshAdapt)\n",
"Info : [ 50%] Meshing surface 11 (Plane, MeshAdapt)\n",
"Info : [ 60%] Meshing surface 12 (Plane, MeshAdapt)\n",
"Info : [ 70%] Meshing surface 13 (Plane, MeshAdapt)\n",
"Info : [ 80%] Meshing surface 14 (Plane, MeshAdapt)\n",
"Info : [ 90%] Meshing surface 15 (Plane, MeshAdapt)\n",
"Info : [100%] Meshing surface 16 (Sphere, MeshAdapt)\n",
"Info : Done meshing 2D (Wall 2.3741s, CPU 2.35231s)\n",
"Info : Meshing 3D...\n",
"Info : 3D Meshing 2 volumes with 1 connected component\n",
"Info : Tetrahedrizing 7351 nodes...\n",
"Info : Done tetrahedrizing 7359 nodes (Wall 0.0740404s, CPU 0.069042s)\n",
"Info : Reconstructing mesh...\n",
"Info : - Creating surface mesh\n",
"Info : - Identifying boundary edges\n",
"Info : - Recovering boundary\n",
"Info : Done reconstructing mesh (Wall 0.215381s, CPU 0.197498s)\n",
"Info : Found volume 2\n",
"Info : Found volume 1\n",
"Info : It. 0 - 0 nodes created - worst tet radius 15.8281 (nodes removed 0 0)\n",
"Info : It. 500 - 500 nodes created - worst tet radius 3.01409 (nodes removed 0 0)\n",
"Info : It. 1000 - 1000 nodes created - worst tet radius 2.48289 (nodes removed 0 0)\n",
"Info : It. 1500 - 1500 nodes created - worst tet radius 2.19831 (nodes removed 0 0)\n",
"Info : It. 2000 - 2000 nodes created - worst tet radius 2.01023 (nodes removed 0 0)\n",
"Info : It. 2500 - 2500 nodes created - worst tet radius 1.87804 (nodes removed 0 0)\n",
"Info : It. 3000 - 3000 nodes created - worst tet radius 1.77311 (nodes removed 0 0)\n",
"Info : It. 3500 - 3500 nodes created - worst tet radius 1.6934 (nodes removed 0 0)\n",
"Info : It. 4000 - 4000 nodes created - worst tet radius 1.62406 (nodes removed 0 0)\n",
"Info : It. 4500 - 4500 nodes created - worst tet radius 1.56586 (nodes removed 0 0)\n",
"Info : It. 5000 - 5000 nodes created - worst tet radius 1.51457 (nodes removed 0 0)\n",
"Info : It. 5500 - 5500 nodes created - worst tet radius 1.4705 (nodes removed 0 0)\n",
"Info : It. 6000 - 6000 nodes created - worst tet radius 1.43014 (nodes removed 0 0)\n",
"Info : It. 6500 - 6500 nodes created - worst tet radius 1.39468 (nodes removed 0 0)\n",
"Info : It. 7000 - 7000 nodes created - worst tet radius 1.36281 (nodes removed 0 0)\n",
"Info : It. 7500 - 7500 nodes created - worst tet radius 1.33488 (nodes removed 0 0)\n",
"Info : It. 8000 - 8000 nodes created - worst tet radius 1.30946 (nodes removed 0 0)\n",
"Info : It. 8500 - 8500 nodes created - worst tet radius 1.28468 (nodes removed 0 0)\n",
"Info : It. 9000 - 9000 nodes created - worst tet radius 1.26165 (nodes removed 0 0)\n",
"Info : It. 9500 - 9500 nodes created - worst tet radius 1.24006 (nodes removed 0 0)\n",
"Info : It. 10000 - 10000 nodes created - worst tet radius 1.21952 (nodes removed 0 0)\n",
"Info : It. 10500 - 10500 nodes created - worst tet radius 1.20277 (nodes removed 0 0)\n",
"Info : It. 11000 - 11000 nodes created - worst tet radius 1.18561 (nodes removed 0 0)\n",
"Info : It. 11500 - 11500 nodes created - worst tet radius 1.16931 (nodes removed 0 0)\n",
"Info : It. 12000 - 12000 nodes created - worst tet radius 1.15293 (nodes removed 0 0)\n",
"Info : It. 12500 - 12500 nodes created - worst tet radius 1.13751 (nodes removed 0 0)\n",
"Info : It. 13000 - 13000 nodes created - worst tet radius 1.12296 (nodes removed 0 0)\n",
"Info : It. 13500 - 13500 nodes created - worst tet radius 1.1098 (nodes removed 0 0)\n",
"Info : It. 14000 - 14000 nodes created - worst tet radius 1.09709 (nodes removed 0 0)\n",
"Info : It. 14500 - 14500 nodes created - worst tet radius 1.08546 (nodes removed 0 0)\n",
"Info : It. 15000 - 15000 nodes created - worst tet radius 1.07404 (nodes removed 0 0)\n",
"Info : It. 15500 - 15500 nodes created - worst tet radius 1.0625 (nodes removed 0 0)\n",
"Info : It. 16000 - 16000 nodes created - worst tet radius 1.05158 (nodes removed 0 0)\n",
"Info : It. 16500 - 16500 nodes created - worst tet radius 1.04114 (nodes removed 0 0)\n",
"Info : It. 17000 - 17000 nodes created - worst tet radius 1.03064 (nodes removed 0 0)\n",
"Info : It. 17500 - 17500 nodes created - worst tet radius 1.02124 (nodes removed 0 0)\n",
"Info : It. 18000 - 18000 nodes created - worst tet radius 1.01253 (nodes removed 0 0)\n",
"Info : It. 18500 - 18500 nodes created - worst tet radius 1.0038 (nodes removed 0 0)\n",
"Info : 3D refinement terminated (26079 nodes total):\n",
"Info : - 1 Delaunay cavities modified for star shapeness\n",
"Info : - 0 nodes could not be inserted\n",
"Info : - 147911 tetrahedra created in 1.26757 sec. (116688 tets/s)\n",
"Info : 0 node relocations\n",
"Info : Done meshing 3D (Wall 1.88412s, CPU 1.86293s)\n",
"Info : Optimizing mesh...\n",
"Info : Optimizing volume 1\n",
"Info : Optimization starts (volume = 4.68e-06) with worst = 0.043499 / average = 0.765452:\n",
"Info : 0.00 < quality < 0.10 : 11 elements\n",
"Info : 0.10 < quality < 0.20 : 42 elements\n",
"Info : 0.20 < quality < 0.30 : 58 elements\n",
"Info : 0.30 < quality < 0.40 : 76 elements\n",
"Info : 0.40 < quality < 0.50 : 113 elements\n",
"Info : 0.50 < quality < 0.60 : 224 elements\n",
"Info : 0.60 < quality < 0.70 : 797 elements\n",
"Info : 0.70 < quality < 0.80 : 1513 elements\n",
"Info : 0.80 < quality < 0.90 : 1954 elements\n",
"Info : 0.90 < quality < 1.00 : 686 elements\n",
"Info : 109 edge swaps, 0 node relocations (volume = 4.68e-06): worst = 0.170489 / average = 0.776728 (Wall 0.00127495s, CPU 0.001333s)\n",
"Info : 111 edge swaps, 0 node relocations (volume = 4.68e-06): worst = 0.170489 / average = 0.776554 (Wall 0.00161795s, CPU 0.001698s)\n",
"Info : No ill-shaped tets in the mesh :-)\n",
"Info : 0.00 < quality < 0.10 : 0 elements\n",
"Info : 0.10 < quality < 0.20 : 1 elements\n",
"Info : 0.20 < quality < 0.30 : 1 elements\n",
"Info : 0.30 < quality < 0.40 : 78 elements\n",
"Info : 0.40 < quality < 0.50 : 110 elements\n",
"Info : 0.50 < quality < 0.60 : 215 elements\n",
"Info : 0.60 < quality < 0.70 : 809 elements\n",
"Info : 0.70 < quality < 0.80 : 1521 elements\n",
"Info : 0.80 < quality < 0.90 : 1956 elements\n",
"Info : 0.90 < quality < 1.00 : 684 elements\n",
"Info : Optimizing volume 2\n",
"Info : Optimization starts (volume = 0.000691485) with worst = 0.00995949 / average = 0.774371:\n",
"Info : 0.00 < quality < 0.10 : 299 elements\n",
"Info : 0.10 < quality < 0.20 : 929 elements\n",
"Info : 0.20 < quality < 0.30 : 1647 elements\n",
"Info : 0.30 < quality < 0.40 : 2640 elements\n",
"Info : 0.40 < quality < 0.50 : 4182 elements\n",
"Info : 0.50 < quality < 0.60 : 7314 elements\n",
"Info : 0.60 < quality < 0.70 : 15270 elements\n",
"Info : 0.70 < quality < 0.80 : 32557 elements\n",
"Info : 0.80 < quality < 0.90 : 51512 elements\n",
"Info : 0.90 < quality < 1.00 : 26087 elements\n",
"Info : 2833 edge swaps, 108 node relocations (volume = 0.000691485): worst = 0.146052 / average = 0.786592 (Wall 0.0896043s, CPU 0.090486s)\n",
"Info : 2850 edge swaps, 110 node relocations (volume = 0.000691485): worst = 0.249473 / average = 0.786642 (Wall 0.117308s, CPU 0.118229s)\n",
"Info : No ill-shaped tets in the mesh :-)\n",
"Info : 0.00 < quality < 0.10 : 0 elements\n",
"Info : 0.10 < quality < 0.20 : 0 elements\n",
"Info : 0.20 < quality < 0.30 : 7 elements\n",
"Info : 0.30 < quality < 0.40 : 2648 elements\n",
"Info : 0.40 < quality < 0.50 : 4039 elements\n",
"Info : 0.50 < quality < 0.60 : 7230 elements\n",
"Info : 0.60 < quality < 0.70 : 15182 elements\n",
"Info : 0.70 < quality < 0.80 : 32926 elements\n",
"Info : 0.80 < quality < 0.90 : 51938 elements\n",
"Info : 0.90 < quality < 1.00 : 25960 elements\n",
"Info : Done optimizing mesh (Wall 0.34924s, CPU 0.326631s)\n",
"Info : 26079 nodes 160343 elements\n",
"Info : Optimizing mesh (Netgen)...\n",
"Info : Optimizing volume 1\n",
"Info : CalcLocalH: 1847 Points 5377 Elements 3682 Surface Elements \n",
"Info : Remove Illegal Elements \n",
"Info : 399 illegal tets \n",
"Info : SplitImprove \n",
"Info : badmax = 79.1788 \n",
"Info : 55 splits performed \n",
"Info : SwapImprove \n",
"Info : 66 swaps performed \n",
"Info : SwapImprove2 \n",
"Info : 1 swaps performed \n",
"Info : 311 illegal tets \n",
"Info : SplitImprove \n",
"Info : badmax = 30.1979 \n",
"Info : 60 splits performed \n",
"Info : SwapImprove \n",
"Info : 32 swaps performed \n",
"Info : SwapImprove2 \n",
"Info : 6 swaps performed \n",
"Info : 167 illegal tets \n",
"Info : SplitImprove \n",
"Info : badmax = 1829.43 \n",
"Info : 44 splits performed \n",
"Info : SwapImprove \n",
"Info : 9 swaps performed \n",
"Info : SwapImprove2 \n",
"Info : 3 swaps performed \n",
"Info : 57 illegal tets \n",
"Info : SplitImprove \n",
"Info : badmax = 3076.72 \n",
"Info : 17 splits performed \n",
"Info : SwapImprove \n",
"Info : 3 swaps performed \n",
"Info : SwapImprove2 \n",
"Info : 0 swaps performed \n",
"Info : 16 illegal tets \n",
"Info : SplitImprove \n",
"Info : badmax = 952.702 \n",
"Info : 3 splits performed \n",
"Info : SwapImprove \n",
"Info : 0 swaps performed \n",
"Info : SwapImprove2 \n",
"Info : 0 swaps performed \n",
"Info : 10 illegal tets \n",
"Info : SplitImprove \n",
"Info : badmax = 952.702 \n",
"Info : 2 splits performed \n",
"Info : SwapImprove \n",
"Info : 0 swaps performed \n",
"Info : SwapImprove2 \n",
"Info : 0 swaps performed \n",
"Info : 7 illegal tets \n",
"Info : SplitImprove \n",
"Info : badmax = 952.702 \n",
"Info : 2 splits performed \n",
"Info : SwapImprove \n",
"Info : 1 swaps performed \n",
"Info : SwapImprove2 \n",
"Info : 0 swaps performed \n",
"Info : 0 illegal tets \n",
"Info : Volume Optimization \n",
"Info : CombineImprove \n",
"Info : 48 elements combined \n",
"Info : ImproveMesh \n",
"Info : Total badness = 9677.41 \n",
"Info : Total badness = 9485.14 \n",
"Info : SplitImprove \n",
"Info : badmax = 36.321 \n",
"Info : 1 splits performed \n",
"Info : ImproveMesh \n",
"Info : Total badness = 9490.21 \n",
"Info : Total badness = 9477.09 \n",
"Info : SwapImprove \n",
"Info : 278 swaps performed \n",
"Info : SwapImprove2 \n",
"Info : 0 swaps performed \n",
"Info : ImproveMesh \n",
"Info : Total badness = 8983.19 \n",
"Info : Total badness = 8900.51 \n",
"Info : CombineImprove \n",
"Info : 6 elements combined \n",
"Info : ImproveMesh \n",
"Info : Total badness = 8843.31 \n",
"Info : Total badness = 8838.64 \n",
"Info : SplitImprove \n",
"Info : badmax = 13.2784 \n",
"Info : 0 splits performed \n",
"Info : ImproveMesh \n",
"Info : Total badness = 8838.64 \n",
"Info : Total badness = 8838.36 \n",
"Info : SwapImprove \n",
"Info : 40 swaps performed \n",
"Info : SwapImprove2 \n",
"Info : 0 swaps performed \n",
"Info : ImproveMesh \n",
"Info : Total badness = 8768.92 \n",
"Info : Total badness = 8747.16 \n",
"Info : CombineImprove \n",
"Info : 3 elements combined \n",
"Info : ImproveMesh \n",
"Info : Total badness = 8723.24 \n",
"Info : Total badness = 8721.58 \n",
"Info : SplitImprove \n",
"Info : badmax = 13.2756 \n",
"Info : 0 splits performed \n",
"Info : ImproveMesh \n",
"Info : Total badness = 8721.58 \n",
"Info : Total badness = 8721.53 \n",
"Info : SwapImprove \n",
"Info : 20 swaps performed \n",
"Info : SwapImprove2 \n",
"Info : 0 swaps performed \n",
"Info : ImproveMesh \n",
"Info : Total badness = 8699.54 \n",
"Info : Total badness = 8688.24 \n",
"Info : Optimizing volume 2\n",
"Info : CalcLocalH: 26075 Points 139930 Elements 14694 Surface Elements \n",
"Info : Remove Illegal Elements \n",
"Info : 0 illegal tets \n",
"Info : Volume Optimization \n",
"Info : CombineImprove \n",
"Info : 1265 elements combined \n",
"Info : ImproveMesh \n",
"Info : Total badness = 181848 \n",
"Info : Total badness = 173241 \n",
"Info : SplitImprove \n",
"Info : badmax = 14.1834 \n",
"Info : 0 splits performed \n",
"Info : ImproveMesh \n",
"Info : Total badness = 173241 \n",
"Info : Total badness = 171897 \n",
"Info : SwapImprove \n",
"Info : 7804 swaps performed \n",
"Info : SwapImprove2 \n",
"Info : 0 swaps performed \n",
"Info : ImproveMesh \n",
"Info : Total badness = 158135 \n",
"Info : Total badness = 154358 \n",
"Info : CombineImprove \n",
"Info : 287 elements combined \n",
"Info : ImproveMesh \n",
"Info : Total badness = 151838 \n",
"Info : Total badness = 151261 \n",
"Info : SplitImprove \n",
"Info : badmax = 8.91933 \n",
"Info : 0 splits performed \n",
"Info : ImproveMesh \n",
"Info : Total badness = 151261 \n",
"Info : Total badness = 151150 \n",
"Info : SwapImprove \n",
"Info : 952 swaps performed \n",
"Info : SwapImprove2 \n",
"Info : 0 swaps performed \n",
"Info : ImproveMesh \n",
"Info : Total badness = 150467 \n",
"Info : Total badness = 149885 \n",
"Info : CombineImprove \n",
"Info : 56 elements combined \n",
"Info : ImproveMesh \n",
"Info : Total badness = 149406 \n",
"Info : Total badness = 149297 \n",
"Info : SplitImprove \n",
"Info : badmax = 7.26293 \n",
"Info : 0 splits performed \n",
"Info : ImproveMesh \n",
"Info : Total badness = 149297 \n",
"Info : Total badness = 149269 \n",
"Info : SwapImprove \n",
"Info : 268 swaps performed \n",
"Info : SwapImprove2 \n",
"Info : 0 swaps performed \n",
"Info : ImproveMesh \n",
"Info : Total badness = 149165 \n",
"Info : Total badness = 148999 \n",
"Info : Done optimizing mesh (Wall 7.31954s, CPU 7.3046s)\n",
"Info : Writing 'open_ended_antenna.msh'...\n",
"Mesh saved to open_ended_antenna.mshInfo : Done writing 'open_ended_antenna.msh'\n",
"\n",
" Nodes: 24598\n",
" Elements: 144515\n"
]
}
],
"source": [
"# Define the entities which later will become the physical groups.\n",
"entities = [\n",
" Entity(\"air_sphere\", dim=3, btype=\"dielectric\", mesh_order=2, tags=[air_sphere], eps_r=1.0, mu_r=1.0, loss_tan=0.0),\n",
" Entity(\"substrate\", dim=3, btype=\"dielectric\", mesh_order=1, tags=[substrate], eps_r=2.2, mu_r=1.0, loss_tan=0.0009),\n",
" Entity(\"top_conductor\", dim=2, btype=\"pec\", mesh_order=1, tags=[strip_line_1]),\n",
" Entity(\"ground_plane\", dim=2, btype=\"pec\", mesh_order=1, tags=[ground_plane]),\n",
" Entity(\"lumped_port\", dim=2, btype=\"lumped_port\", mesh_order=0, tags=[lumped_port], R=50.0, direction=\"+Z\")\n",
"]\n",
"\n",
"# Boolean operations to guarantee a nice mesh, algo it returns the\n",
"# physical group map.\n",
"pg_map = run_meshing_pipeline(entities)\n",
"\n",
"# Refine near the top conductor and locally the lumped port\n",
"refine_near_surfaces(entities[2].dimtags, \n",
" wavelength, \n",
" ppw_near=50, \n",
" ppw_far=30, \n",
" set_as_background=True,\n",
" local_refinements = {entities[-1].dimtags[0]: 150})\n",
"# Mesh sizes\n",
"mesh_sizes = {\n",
" \"substrate\": wavelength / 12,\n",
" \"air_sphere\": wavelength / 4,\n",
" \"lumped_port\": wavelength / 150,\n",
" \"ground_plane\" : wavelength / 10,\n",
" \"top_conductor\": wavelength / 50\n",
"}\n",
"\n",
"# Generate the 3d mesh.\n",
"generate_3d_mesh(entities, mesh_sizes, filename, optimize = True)"
]
},
{
"cell_type": "markdown",
"id": "8db52b35",
"metadata": {
"papermill": {
"duration": 0.003364,
"end_time": "2026-05-26T01:20:31.885505+00:00",
"exception": false,
"start_time": "2026-05-26T01:20:31.882141+00:00",
"status": "completed"
},
"tags": []
},
"source": [
"### Mesh visualization."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "89d4552b",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-26T01:20:31.894138Z",
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"start_time": "2026-05-26T01:20:31.888751+00:00",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Loading mesh file: open_ended_antenna.msh\n",
"Groups to render transparent: air_sphere__None\n",
"\n",
"Mesh loaded successfully with 2 cell blocks\n",
"Found 14694 triangles total\n",
"Physical group tags in mesh: {3: 'top_conductor', 4: 'ground_plane', 5: 'lumped_port', 6: 'air_sphere__None', 7: 'air_sphere__substrate'}\n"
]
},
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"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
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"output_type": "display_data"
}
],
"source": [
"# Render the physical groups. The air sphere is rendered transparent.\n",
"view_mesh(filename, transparent_groups= \"air_sphere__None\")"
]
},
{
"cell_type": "markdown",
"id": "28ef1749",
"metadata": {
"papermill": {
"duration": 0.006459,
"end_time": "2026-05-26T01:20:33.206636+00:00",
"exception": false,
"start_time": "2026-05-26T01:20:33.200177+00:00",
"status": "completed"
},
"tags": []
},
"source": [
"### Generate palace JSON config"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "45a75202",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-26T01:20:33.221755Z",
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"status": "completed"
},
"tags": []
},
"outputs": [],
"source": [
"config_filename: str = \"op_spalace.conf\"\n",
"freq_min: float = 3.0\n",
"freq_max: float = 3.5\n",
"freq_step: float = 0.005\n",
"eps_r: float = 2.2\n",
"loss_tan: float = 0.0009\n",
"port_impedance: float = 50.0\n",
"solver_order: int = 2"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "8f221339",
"metadata": {
"execution": {
"iopub.execute_input": "2026-05-26T01:20:33.244706Z",
"iopub.status.busy": "2026-05-26T01:20:33.244480Z",
"iopub.status.idle": "2026-05-26T01:20:33.251613Z",
"shell.execute_reply": "2026-05-26T01:20:33.250586Z"
},
"papermill": {
"duration": 0.016058,
"end_time": "2026-05-26T01:20:33.252695+00:00",
"exception": false,
"start_time": "2026-05-26T01:20:33.236637+00:00",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Palace config written to op_spalace.conf\n",
"Wrote op_spalace.conf\n"
]
}
],
"source": [
"sim = Simulation()\n",
"\n",
"def attr(name):\n",
" return [pg_map[name]] if name in pg_map else []\n",
"\n",
"sim.set_mesh_file(f\"/work/{filename}\")\n",
"sim.set_config_option(\"Problem.Output\", \"/work/results/open_ended_antenna/\")\n",
"\n",
"sim.set_config_option(\"Domains.Materials\", [\n",
" {\n",
" \"Attributes\": attr(\"substrate\"),\n",
" \"Permittivity\": eps_r,\n",
" \"Permeability\": 1.0,\n",
" \"LossTan\": loss_tan\n",
" },\n",
" {\n",
" \"Attributes\": attr(\"air\"),\n",
" \"Permittivity\": 1.0,\n",
" \"Permeability\": 1.0\n",
" }\n",
"])\n",
"\n",
"sim.set_config_option(\"Boundaries.PEC\", {\n",
" \"Attributes\": attr(\"ground_plane\") + attr(\"patch\")\n",
"})\n",
"\n",
"sim.set_config_option(\"Boundaries.LumpedPort\", [\n",
" {\n",
" \"Index\": 1,\n",
" \"Attributes\": attr(\"lumped_port\"),\n",
" \"R\": port_impedance,\n",
" \"Excitation\": True,\n",
" \"Direction\": \"+Z\"\n",
" }\n",
"])\n",
"sim.set_config_option(\"Boundaries.Absorbing\", {\n",
" \"Attributes\": attr(\"farfield\"),\n",
" \"Order\": 1\n",
"})\n",
"\n",
"sim.set_config_option(\"Solver.Order\", solver_order)\n",
"sim.set_config_option(\"Solver.Driven.MinFreq\", freq_min)\n",
"sim.set_config_option(\"Solver.Driven.MaxFreq\", freq_max)\n",
"sim.set_config_option(\"Solver.Driven.FreqStep\", freq_step)\n",
"sim.set_config_option(\"Solver.Driven.AdaptiveTol\", 0.001)\n",
"\n",
"config_path = sim.write_config(config_filename)\n",
"print(f\"Wrote {config_path}\")"
]
}
],
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