{
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"source": [
"### Step in depth antenna\n",
"\n",
"A step in width microstrip antenna is a design variation where the radiating patch element has a non-uniform width that changes along its length. Instead of a simple rectangular patch, the conducting strip gradually narrows or widens at specific points."
]
},
{
"cell_type": "code",
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"id": "3588684c",
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"source": [
"import gmsh\n",
"import math\n",
"import os\n",
"from pathlib import Path\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, run_palace"
]
},
{
"cell_type": "markdown",
"id": "35e745ba",
"metadata": {
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"duration": 0.003934,
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"source": [
"### Parameters:\n",
"\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_near_port: Notch width along x-axis near the port, specified as a scalar in meters. \n",
"- strip_lined_width_far: Strip line width along y-axis far from the port, specified as a scalar in meters.\n",
"- air_height : Air box height along z-axis, specified as a scalar in meters. \n",
"- air_margin : Air box margin along x and y axes, 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."
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "31e252bf",
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"source": [
"l1: float = 0.06\n",
"w1: float = 0.06\n",
"strip_line_length: float = 0.06\n",
"strip_line_width_near_port: float = 0.001\n",
"strip_line_width_far: float = 0.003\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 = \"sw_antenna.msh\"\n",
"\n",
"wavelength = 3e8 / (freq * 1e9)"
]
},
{
"cell_type": "markdown",
"id": "9f0c809a",
"metadata": {
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"duration": 0.001131,
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"tags": []
},
"source": [
"### Initialize the model"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "20a8fc36",
"metadata": {
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"status": "completed"
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"tags": []
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"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning : Gmsh has aleady been initialized\n"
]
}
],
"source": [
"gmsh.initialize()\n",
"gmsh.model.add(\"patch_antenna\")\n",
"kernel = gmsh.model.occ"
]
},
{
"cell_type": "markdown",
"id": "e39ac1fa",
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"tags": []
},
"source": [
"### Geometry generation\n"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "f07ee82e",
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"status": "completed"
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"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Info : Cannot bind existing OpenCASCADE surface 8 to second tag 9 \n",
"Info : Could not preserve tag of 2D object 9 (->8)\n"
]
}
],
"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 = kernel.addBox(-l1/2, -w1/2, 0, l1, w1, h)\n",
"\n",
"ground_plane = kernel.addRectangle(-l1/2, -w1/2, 0, l1, w1)\n",
"\n",
"strip_line_1 = kernel.addRectangle(-l1/2, -strip_line_width_near_port/2, h, strip_line_length/2, strip_line_width_near_port)\n",
"strip_line_2 = kernel.addRectangle(0, -strip_line_width_far/2, h, strip_line_length/2, strip_line_width_far)\n",
"\n",
"top_conductor, _ = kernel.fuse(\n",
" [(2, strip_line_1)], [(2, strip_line_2)],\n",
" removeObject=True, removeTool=True\n",
")\n",
"kernel.synchronize()\n",
"\n",
"gap = 0\n",
"lumped_port = kernel.addRectangle(-l1/2 + gap, -strip_line_width_near_port/2, 0, h - gap, strip_line_width_near_port)\n",
"kernel.rotate([(2, lumped_port)], -l1/2, 0, 0, 0, 1, 0, -math.pi/2)\n",
"kernel.synchronize()\n",
"\n",
"# Replace box with an enclosing air sphere, following the patch_antenna pattern.\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",
"kernel.synchronize()"
]
},
{
"cell_type": "markdown",
"id": "4103d2c6",
"metadata": {
"papermill": {
"duration": 0.001258,
"end_time": "2026-05-27T20:02:11.652369+00:00",
"exception": false,
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"status": "completed"
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"tags": []
},
"source": [
"### Entities definition"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "83500869",
"metadata": {
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"status": "completed"
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"tags": []
},
"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=[17]\n",
" Physical group 'air_sphere__substrate' (dim=2): pg=7, tags=[10, 11, 13, 15, 16, 14, 12]\n",
" ppw_near=50 ppw_far=30\n",
" SizeMax=0.0030 transition=0.0227\n",
" global: 8 curves, SizeMin=0.0018\n",
" local (2, 9): 4 curves, SizeMin=0.0006\n",
" Merged 2 fields with Min → field 5\n",
"[Entity('air_sphere', dim=3, order=2, tags=[2]), Entity('substrate', dim=3, order=1, tags=[1]), Entity('top_conductor', dim=2, order=1, tags=[8]), Entity('ground_plane', dim=2, order=1, tags=[7]), Entity('lumped_port', dim=2, order=0, tags=[9])]\n",
"Loading mesh file: sw_antenna.msh\n",
"Groups to render transparent: air_sphere__None\n",
"\n",
"Mesh loaded successfully with 2 cell blocks\n",
"Found 14864 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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""
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"source": [
"# Material and port constants reused in meshing/config sections.\n",
"eps_r: float = 2.2\n",
"loss_tan: float = 0.0009\n",
"port_impedance: float = 50.0\n",
"\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=eps_r, mu_r=1.0, loss_tan=loss_tan),\n",
" Entity(\"top_conductor\", dim=2, btype=\"pec\", mesh_order=1, tags=[top_conductor[0][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=port_impedance, direction=\"+Z\", excitation=True),\n",
"]\n",
"\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",
"\n",
"print(entities)\n",
"\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_3d_mesh(entities, mesh_sizes, filename, optimize=True, verbose=False)\n",
"\n",
"view_mesh(filename, transparent_groups=\"air_sphere__None\")"
]
},
{
"cell_type": "markdown",
"id": "c57f3dcf",
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"status": "completed"
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"tags": []
},
"source": [
"### Generate JSON config\n"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "770fd071",
"metadata": {
"execution": {
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"status": "completed"
},
"tags": []
},
"outputs": [],
"source": [
"output_file: str = \"sw_antenna.json\"\n",
"freq_min: float = 3.0\n",
"freq_max: float = 3.5\n",
"freq_step: float = 0.005\n",
"solver_order: int = 2"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "c7e87f93",
"metadata": {
"execution": {
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"status": "completed"
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},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Palace config written to /home/martin/Desktop/PalaceToolkit/docs/examples/sw_antenna.json\n",
" Running: apptainer exec --pwd /work --bind /home/martin/Desktop/PalaceToolkit/docs/examples:/work /opt/palace/Palace.sif mpirun -np 8 /opt/palace/bin/palace-x86_64.bin /work/sw_antenna.json\n",
"\n",
"_____________ _______\n",
"_____ __ \\____ __ /____ ____________\n",
"____ /_/ / __ ` / / __ ` / ___/ _ \\\n",
"___ _____/ /_/ / / /_/ / /__/ ___/\n",
" /__/ \\___,__/__/\\___,__/\\_____\\_____/\n",
"\n",
"\n",
"\u001b[38;2;255;255;000m--> Warning!\u001b[0m\n",
"Output folder is not empty; program will overwrite content! (postpro/sw_antenna)\n",
"Git changeset ID: v0.14.0-270-g9d6ea72f\n",
"Running with 8 MPI processes, 1 OpenMP thread\n",
"Device configuration: omp,cpu\n",
"Memory configuration: host-std\n",
"libCEED backend: /cpu/self/xsmm/blocked\n",
"\n",
"Removed 126398 unmarked domain elements from the mesh\n",
"Removed 11012 unattached boundary elements from the mesh\n",
"\n",
"\u001b[38;2;255;255;000m--> Warning!\u001b[0m\n",
"One or more external boundary attributes has no associated boundary condition!\n",
"\"PMC\"/\"ZeroCharge\" condition is assumed!\n",
"\n",
"Boundary attribute list: 7, 3\n",
"\n",
"Finished partitioning mesh into 8 subdomains\n",
"\n",
"Characteristic length and time scales:\n",
" L₀ = 6.000e-02 m, t₀ = 2.001e-01 ns\n",
"\n",
"Mesh curvature order: 1\n",
"Mesh bounding box:\n",
" (Xmin, Ymin, Zmin) = (-3.000e-02, -3.000e-02, +0.000e+00) m\n",
" (Xmax, Ymax, Zmax) = (+3.000e-02, +3.000e-02, +1.300e-03) m\n",
"\n",
"Parallel Mesh Stats:\n",
"\n",
" minimum average maximum total\n",
" vertices 225 258 279 2067\n",
" edges 1219 1279 1346 10234\n",
" faces 1774 1801 1872 14410\n",
" elements 770 780 803 6242\n",
" neighbors 2 3 5\n",
"\n",
" minimum maximum\n",
" h 0.00606189 0.0455948\n",
" kappa 1.08749 7.06351\n",
"\n",
"Configuring Robin impedance BC for lumped ports at attributes:\n",
" 5: Rs = 3.846e+01 Ω/sq, n = (-1.0,+0.0,+0.0)\n",
"\n",
"Configuring lumped port circuit properties:\n",
" Index = 1: R = 5.000e+01 Ω\n",
"\n",
"Configuring lumped port excitation source term at attributes:\n",
" 5: Index = 1\n",
"\n",
"Configuring Dirichlet PEC BC at attributes:\n",
" 4\n",
"\n",
"Computing adaptive fast frequency response for:\n",
"Excitation with index 1 has contributions from:\n",
" Lumped port 1\n",
"\n",
"Beginning PROM construction offline phase:\n",
" 101 points for frequency sweep over [3.000e+00, 3.500e+00] GHz\n",
"\n",
"Assembling system matrices, number of global unknowns:\n",
" H1 (p = 2): 12301, ND (p = 2): 49288, RT (p = 2): 61956\n",
" Operator assembly level: Partial\n",
" Mesh geometries:\n",
" Tetrahedron: P = 20, Q = 11 (quadrature order = 4)\n",
"\n",
"Assembling multigrid hierarchy:\n",
" Level 0 (p = 1): 10234 unknowns\n",
" Level 1 (p = 2): 49288 unknowns\n",
" Level 0 (auxiliary) (p = 1): 2067 unknowns\n",
" Level 1 (auxiliary) (p = 2): 12301 unknowns\n",
"\n",
" Residual norms for GMRES solve\n",
" 0 (restart 0) KSP residual norm 5.881703e+00\n",
" 1 (restart 0) KSP residual norm 5.106262e-01\n",
" 2 (restart 0) KSP residual norm 6.153197e-02\n",
" 3 (restart 0) KSP residual norm 4.190902e-03\n",
" 4 (restart 0) KSP residual norm 3.373165e-04\n",
" 5 (restart 0) KSP residual norm 8.506839e-05\n",
" 6 (restart 0) KSP residual norm 1.716645e-05\n",
" 7 (restart 0) KSP residual norm 4.601451e-06\n",
" 8 (restart 0) KSP residual norm 8.160670e-07\n",
" 9 (restart 0) KSP residual norm 2.338796e-07\n",
" 10 (restart 0) KSP residual norm 4.650858e-08\n",
"GMRES solver converged in 10 iterations (avg. reduction factor: 1.548e-01)\n",
" Field energy E (2.060e-03 J) + H (9.714e-06 J) = 2.070e-03 J\n",
"\n",
" Residual norms for GMRES solve\n",
" 0 (restart 0) KSP residual norm 5.890474e+00\n",
" 1 (restart 0) KSP residual norm 5.117230e-01\n",
" 2 (restart 0) KSP residual norm 6.168093e-02\n",
" 3 (restart 0) KSP residual norm 4.212283e-03\n",
" 4 (restart 0) KSP residual norm 3.590536e-04\n",
" 5 (restart 0) KSP residual norm 9.721376e-05\n",
" 6 (restart 0) KSP residual norm 1.875633e-05\n",
" 7 (restart 0) KSP residual norm 5.254566e-06\n",
" 8 (restart 0) KSP residual norm 9.283490e-07\n",
" 9 (restart 0) KSP residual norm 2.660571e-07\n",
" 10 (restart 0) KSP residual norm 5.663171e-08\n",
"GMRES solver converged in 10 iterations (avg. reduction factor: 1.579e-01)\n",
" Field energy E (2.067e-03 J) + H (1.328e-05 J) = 2.080e-03 J\n",
"\n",
" Residual norms for GMRES solve\n",
" 0 (restart 0) KSP residual norm 5.886077e+00\n",
" 1 (restart 0) KSP residual norm 5.111730e-01\n",
" 2 (restart 0) KSP residual norm 6.160628e-02\n",
" 3 (restart 0) KSP residual norm 4.201554e-03\n",
" 4 (restart 0) KSP residual norm 3.482888e-04\n",
" 5 (restart 0) KSP residual norm 9.142889e-05\n",
" 6 (restart 0) KSP residual norm 1.797813e-05\n",
" 7 (restart 0) KSP residual norm 4.943300e-06\n",
" 8 (restart 0) KSP residual norm 8.730091e-07\n",
" 9 (restart 0) KSP residual norm 2.504677e-07\n",
" 10 (restart 0) KSP residual norm 5.159699e-08\n",
"GMRES solver converged in 10 iterations (avg. reduction factor: 1.564e-01)\n",
"\n",
"Greedy iteration 1 (n = 4): ω* = 3.259e+00 GHz (4.098e+00), error = 1.012e-07, memory = 1/2\n",
" Field energy E (2.063e-03 J) + H (1.149e-05 J) = 2.075e-03 J\n",
"\n",
" Residual norms for GMRES solve\n",
" 0 (restart 0) KSP residual norm 5.883493e+00\n",
" 1 (restart 0) KSP residual norm 5.108499e-01\n",
" 2 (restart 0) KSP residual norm 6.156238e-02\n",
" 3 (restart 0) KSP residual norm 4.195257e-03\n",
" 4 (restart 0) KSP residual norm 3.418391e-04\n",
" 5 (restart 0) KSP residual norm 8.775320e-05\n",
" 6 (restart 0) KSP residual norm 1.750387e-05\n",
" 7 (restart 0) KSP residual norm 4.745755e-06\n",
" 8 (restart 0) KSP residual norm 8.396276e-07\n",
" 9 (restart 0) KSP residual norm 2.408297e-07\n",
" 10 (restart 0) KSP residual norm 4.860196e-08\n",
"GMRES solver converged in 10 iterations (avg. reduction factor: 1.555e-01)\n",
"\n",
"Greedy iteration 2 (n = 6): ω* = 3.109e+00 GHz (3.909e+00), error = 2.537e-09, memory = 2/2\n",
" Field energy E (2.062e-03 J) + H (1.044e-05 J) = 2.072e-03 J\n",
"\n",
"Adaptive sampling converged with 4 frequency samples:\n",
" n = 8, error = 2.537e-09, tol = 1.000e-03, memory = 2/2\n",
" Sampled frequencies (GHz): 3.000e+00, 3.500e+00, 3.259e+00, 3.109e+00\n",
" Sample errors: inf, inf, 1.012e-07, 2.537e-09\n",
" Total offline phase elapsed time: 5.84e+00 s\n",
"\n",
"Beginning fast frequency sweep online phase\n",
"\n",
"It 1/101: ω/2π = 3.000e+00 GHz (total elapsed time = 5.84e+00 s)\n",
"\n",
" Sol. ||E|| = 6.020480e+00\n",
" Field energy E (2.060e-03 J) + H (9.714e-06 J) = 2.070e-03 J\n",
" S[1][1] = +9.991e-01-3.865e-02i, |S[1][1]| = -1.357e-03, arg(S[1][1]) = -2.215e+00\n",
"\n",
"It 2/101: ω/2π = 3.005e+00 GHz (total elapsed time = 5.85e+00 s)\n",
"\n",
" Sol. ||E|| = 6.020561e+00\n",
" Field energy E (2.060e-03 J) + H (9.747e-06 J) = 2.070e-03 J\n",
" S[1][1] = +9.991e-01-3.872e-02i, |S[1][1]| = -1.361e-03, arg(S[1][1]) = -2.219e+00\n",
"\n",
"It 3/101: ω/2π = 3.010e+00 GHz (total elapsed time = 5.85e+00 s)\n",
"\n",
" Sol. ||E|| = 6.020643e+00\n",
" Field energy E (2.060e-03 J) + H (9.780e-06 J) = 2.070e-03 J\n",
" S[1][1] = +9.991e-01-3.878e-02i, |S[1][1]| = -1.366e-03, arg(S[1][1]) = -2.223e+00\n",
"\n",
"It 4/101: ω/2π = 3.015e+00 GHz (total elapsed time = 5.86e+00 s)\n",
"\n",
" Sol. ||E|| = 6.020724e+00\n",
" Field energy E (2.060e-03 J) + H (9.813e-06 J) = 2.070e-03 J\n",
" S[1][1] = +9.991e-01-3.885e-02i, |S[1][1]| = -1.370e-03, arg(S[1][1]) = -2.227e+00\n",
"\n",
"It 5/101: ω/2π = 3.020e+00 GHz (total elapsed time = 5.87e+00 s)\n",
"\n",
" Sol. ||E|| = 6.020806e+00\n",
" Field energy E (2.060e-03 J) + H (9.846e-06 J) = 2.070e-03 J\n",
" S[1][1] = +9.991e-01-3.891e-02i, |S[1][1]| = -1.374e-03, arg(S[1][1]) = -2.230e+00\n",
"\n",
"It 6/101: ω/2π = 3.025e+00 GHz (total elapsed time = 5.87e+00 s)\n",
"\n",
" Sol. ||E|| = 6.020887e+00\n",
" Field energy E (2.060e-03 J) + H (9.879e-06 J) = 2.070e-03 J\n",
" S[1][1] = +9.991e-01-3.898e-02i, |S[1][1]| = -1.378e-03, arg(S[1][1]) = -2.234e+00\n",
"\n",
"It 7/101: ω/2π = 3.030e+00 GHz (total elapsed time = 5.88e+00 s)\n",
"\n",
" Sol. ||E|| = 6.020969e+00\n",
" Field energy E (2.061e-03 J) + H (9.912e-06 J) = 2.070e-03 J\n",
" S[1][1] = +9.991e-01-3.904e-02i, |S[1][1]| = -1.382e-03, arg(S[1][1]) = -2.238e+00\n",
"\n",
"It 8/101: ω/2π = 3.035e+00 GHz (total elapsed time = 5.89e+00 s)\n",
"\n",
" Sol. ||E|| = 6.021051e+00\n",
" Field energy E (2.061e-03 J) + H (9.945e-06 J) = 2.071e-03 J\n",
" S[1][1] = +9.991e-01-3.910e-02i, |S[1][1]| = -1.386e-03, arg(S[1][1]) = -2.241e+00\n",
"\n",
"It 9/101: ω/2π = 3.040e+00 GHz (total elapsed time = 5.89e+00 s)\n",
"\n",
" Sol. ||E|| = 6.021133e+00\n",
" Field energy E (2.061e-03 J) + H (9.978e-06 J) = 2.071e-03 J\n",
" S[1][1] = +9.991e-01-3.917e-02i, |S[1][1]| = -1.390e-03, arg(S[1][1]) = -2.245e+00\n",
"\n",
"It 10/101: ω/2π = 3.045e+00 GHz (total elapsed time = 5.90e+00 s)\n",
"\n",
" Sol. ||E|| = 6.021216e+00\n",
" Field energy E (2.061e-03 J) + H (1.001e-05 J) = 2.071e-03 J\n",
" S[1][1] = +9.991e-01-3.923e-02i, |S[1][1]| = -1.394e-03, arg(S[1][1]) = -2.249e+00\n",
"\n",
"It 11/101: ω/2π = 3.050e+00 GHz (total elapsed time = 5.90e+00 s)\n",
"\n",
" Sol. ||E|| = 6.021298e+00\n",
" Field energy E (2.061e-03 J) + H (1.004e-05 J) = 2.071e-03 J\n",
" S[1][1] = +9.991e-01-3.930e-02i, |S[1][1]| = -1.399e-03, arg(S[1][1]) = -2.253e+00\n",
"\n",
"It 12/101: ω/2π = 3.055e+00 GHz (total elapsed time = 5.91e+00 s)\n",
"\n",
" Sol. ||E|| = 6.021381e+00\n",
" Field energy E (2.061e-03 J) + H (1.008e-05 J) = 2.071e-03 J\n",
" S[1][1] = +9.991e-01-3.936e-02i, |S[1][1]| = -1.403e-03, arg(S[1][1]) = -2.256e+00\n",
"\n",
"It 13/101: ω/2π = 3.060e+00 GHz (total elapsed time = 5.91e+00 s)\n",
"\n",
" Sol. ||E|| = 6.021463e+00\n",
" Field energy E (2.061e-03 J) + H (1.011e-05 J) = 2.071e-03 J\n",
" S[1][1] = +9.991e-01-3.943e-02i, |S[1][1]| = -1.407e-03, arg(S[1][1]) = -2.260e+00\n",
"\n",
"It 14/101: ω/2π = 3.065e+00 GHz (total elapsed time = 5.92e+00 s)\n",
"\n",
" Sol. ||E|| = 6.021546e+00\n",
" Field energy E (2.061e-03 J) + H (1.014e-05 J) = 2.071e-03 J\n",
" S[1][1] = +9.991e-01-3.949e-02i, |S[1][1]| = -1.411e-03, arg(S[1][1]) = -2.264e+00\n",
"\n",
"It 15/101: ω/2π = 3.070e+00 GHz (total elapsed time = 5.92e+00 s)\n",
"\n",
" Sol. ||E|| = 6.021629e+00\n",
" Field energy E (2.061e-03 J) + H (1.018e-05 J) = 2.071e-03 J\n",
" S[1][1] = +9.991e-01-3.956e-02i, |S[1][1]| = -1.415e-03, arg(S[1][1]) = -2.268e+00\n",
"\n",
"It 16/101: ω/2π = 3.075e+00 GHz (total elapsed time = 5.93e+00 s)\n",
"\n",
" Sol. ||E|| = 6.021712e+00\n",
" Field energy E (2.061e-03 J) + H (1.021e-05 J) = 2.071e-03 J\n",
" S[1][1] = +9.991e-01-3.962e-02i, |S[1][1]| = -1.420e-03, arg(S[1][1]) = -2.271e+00\n",
"\n",
"It 17/101: ω/2π = 3.080e+00 GHz (total elapsed time = 5.93e+00 s)\n",
"\n",
" Sol. ||E|| = 6.021795e+00\n",
" Field energy E (2.061e-03 J) + H (1.025e-05 J) = 2.071e-03 J\n",
" S[1][1] = +9.990e-01-3.969e-02i, |S[1][1]| = -1.424e-03, arg(S[1][1]) = -2.275e+00\n",
"\n",
"It 18/101: ω/2π = 3.085e+00 GHz (total elapsed time = 5.94e+00 s)\n",
"\n",
" Sol. ||E|| = 6.021879e+00\n",
" Field energy E (2.061e-03 J) + H (1.028e-05 J) = 2.072e-03 J\n",
" S[1][1] = +9.990e-01-3.975e-02i, |S[1][1]| = -1.428e-03, arg(S[1][1]) = -2.279e+00\n",
"\n",
"It 19/101: ω/2π = 3.090e+00 GHz (total elapsed time = 5.94e+00 s)\n",
"\n",
" Sol. ||E|| = 6.021962e+00\n",
" Field energy E (2.061e-03 J) + H (1.031e-05 J) = 2.072e-03 J\n",
" S[1][1] = +9.990e-01-3.982e-02i, |S[1][1]| = -1.432e-03, arg(S[1][1]) = -2.282e+00\n",
"\n",
"It 20/101: ω/2π = 3.095e+00 GHz (total elapsed time = 5.95e+00 s)\n",
"\n",
" Sol. ||E|| = 6.022046e+00\n",
" Field energy E (2.061e-03 J) + H (1.035e-05 J) = 2.072e-03 J\n",
" S[1][1] = +9.990e-01-3.988e-02i, |S[1][1]| = -1.436e-03, arg(S[1][1]) = -2.286e+00\n",
"\n",
"It 21/101: ω/2π = 3.100e+00 GHz (total elapsed time = 5.95e+00 s)\n",
"\n",
" Sol. ||E|| = 6.022130e+00\n",
" Field energy E (2.061e-03 J) + H (1.038e-05 J) = 2.072e-03 J\n",
" S[1][1] = +9.990e-01-3.995e-02i, |S[1][1]| = -1.441e-03, arg(S[1][1]) = -2.290e+00\n",
"\n",
"It 22/101: ω/2π = 3.105e+00 GHz (total elapsed time = 5.96e+00 s)\n",
"\n",
" Sol. ||E|| = 6.022213e+00\n",
" Field energy E (2.061e-03 J) + H (1.041e-05 J) = 2.072e-03 J\n",
" S[1][1] = +9.990e-01-4.001e-02i, |S[1][1]| = -1.445e-03, arg(S[1][1]) = -2.294e+00\n",
"\n",
"It 23/101: ω/2π = 3.110e+00 GHz (total elapsed time = 5.96e+00 s)\n",
"\n",
" Sol. ||E|| = 6.022298e+00\n",
" Field energy E (2.062e-03 J) + H (1.045e-05 J) = 2.072e-03 J\n",
" S[1][1] = +9.990e-01-4.008e-02i, |S[1][1]| = -1.449e-03, arg(S[1][1]) = -2.297e+00\n",
"\n",
"It 24/101: ω/2π = 3.115e+00 GHz (total elapsed time = 5.97e+00 s)\n",
"\n",
" Sol. ||E|| = 6.022382e+00\n",
" Field energy E (2.062e-03 J) + H (1.048e-05 J) = 2.072e-03 J\n",
" S[1][1] = +9.990e-01-4.014e-02i, |S[1][1]| = -1.453e-03, arg(S[1][1]) = -2.301e+00\n",
"\n",
"It 25/101: ω/2π = 3.120e+00 GHz (total elapsed time = 5.97e+00 s)\n",
"\n",
" Sol. ||E|| = 6.022466e+00\n",
" Field energy E (2.062e-03 J) + H (1.052e-05 J) = 2.072e-03 J\n",
" S[1][1] = +9.990e-01-4.021e-02i, |S[1][1]| = -1.458e-03, arg(S[1][1]) = -2.305e+00\n",
"\n",
"It 26/101: ω/2π = 3.125e+00 GHz (total elapsed time = 5.98e+00 s)\n",
"\n",
" Sol. ||E|| = 6.022551e+00\n",
" Field energy E (2.062e-03 J) + H (1.055e-05 J) = 2.072e-03 J\n",
" S[1][1] = +9.990e-01-4.028e-02i, |S[1][1]| = -1.462e-03, arg(S[1][1]) = -2.309e+00\n",
"\n",
"It 27/101: ω/2π = 3.130e+00 GHz (total elapsed time = 5.98e+00 s)\n",
"\n",
" Sol. ||E|| = 6.022635e+00\n",
" Field energy E (2.062e-03 J) + H (1.058e-05 J) = 2.072e-03 J\n",
" S[1][1] = +9.990e-01-4.034e-02i, |S[1][1]| = -1.466e-03, arg(S[1][1]) = -2.312e+00\n",
"\n",
"It 28/101: ω/2π = 3.135e+00 GHz (total elapsed time = 5.99e+00 s)\n",
"\n",
" Sol. ||E|| = 6.022720e+00\n",
" Field energy E (2.062e-03 J) + H (1.062e-05 J) = 2.072e-03 J\n",
" S[1][1] = +9.990e-01-4.041e-02i, |S[1][1]| = -1.470e-03, arg(S[1][1]) = -2.316e+00\n",
"\n",
"It 29/101: ω/2π = 3.140e+00 GHz (total elapsed time = 6.00e+00 s)\n",
"\n",
" Sol. ||E|| = 6.022805e+00\n",
" Field energy E (2.062e-03 J) + H (1.065e-05 J) = 2.073e-03 J\n",
" S[1][1] = +9.990e-01-4.047e-02i, |S[1][1]| = -1.475e-03, arg(S[1][1]) = -2.320e+00\n",
"\n",
"It 30/101: ω/2π = 3.145e+00 GHz (total elapsed time = 6.00e+00 s)\n",
"\n",
" Sol. ||E|| = 6.022890e+00\n",
" Field energy E (2.062e-03 J) + H (1.069e-05 J) = 2.073e-03 J\n",
" S[1][1] = +9.990e-01-4.054e-02i, |S[1][1]| = -1.479e-03, arg(S[1][1]) = -2.324e+00\n",
"\n",
"It 31/101: ω/2π = 3.150e+00 GHz (total elapsed time = 6.01e+00 s)\n",
"\n",
" Sol. ||E|| = 6.022975e+00\n",
" Field energy E (2.062e-03 J) + H (1.072e-05 J) = 2.073e-03 J\n",
" S[1][1] = +9.990e-01-4.060e-02i, |S[1][1]| = -1.483e-03, arg(S[1][1]) = -2.327e+00\n",
"\n",
"It 32/101: ω/2π = 3.155e+00 GHz (total elapsed time = 6.01e+00 s)\n",
"\n",
" Sol. ||E|| = 6.023060e+00\n",
" Field energy E (2.062e-03 J) + H (1.076e-05 J) = 2.073e-03 J\n",
" S[1][1] = +9.990e-01-4.067e-02i, |S[1][1]| = -1.488e-03, arg(S[1][1]) = -2.331e+00\n",
"\n",
"It 33/101: ω/2π = 3.160e+00 GHz (total elapsed time = 6.02e+00 s)\n",
"\n",
" Sol. ||E|| = 6.023146e+00\n",
" Field energy E (2.062e-03 J) + H (1.079e-05 J) = 2.073e-03 J\n",
" S[1][1] = +9.990e-01-4.073e-02i, |S[1][1]| = -1.492e-03, arg(S[1][1]) = -2.335e+00\n",
"\n",
"It 34/101: ω/2π = 3.165e+00 GHz (total elapsed time = 6.02e+00 s)\n",
"\n",
" Sol. ||E|| = 6.023231e+00\n",
" Field energy E (2.062e-03 J) + H (1.083e-05 J) = 2.073e-03 J\n",
" S[1][1] = +9.990e-01-4.080e-02i, |S[1][1]| = -1.496e-03, arg(S[1][1]) = -2.338e+00\n",
"\n",
"It 35/101: ω/2π = 3.170e+00 GHz (total elapsed time = 6.03e+00 s)\n",
"\n",
" Sol. ||E|| = 6.023317e+00\n",
" Field energy E (2.062e-03 J) + H (1.086e-05 J) = 2.073e-03 J\n",
" S[1][1] = +9.990e-01-4.086e-02i, |S[1][1]| = -1.500e-03, arg(S[1][1]) = -2.342e+00\n",
"\n",
"It 36/101: ω/2π = 3.175e+00 GHz (total elapsed time = 6.03e+00 s)\n",
"\n",
" Sol. ||E|| = 6.023403e+00\n",
" Field energy E (2.062e-03 J) + H (1.090e-05 J) = 2.073e-03 J\n",
" S[1][1] = +9.990e-01-4.093e-02i, |S[1][1]| = -1.505e-03, arg(S[1][1]) = -2.346e+00\n",
"\n",
"It 37/101: ω/2π = 3.180e+00 GHz (total elapsed time = 6.04e+00 s)\n",
"\n",
" Sol. ||E|| = 6.023489e+00\n",
" Field energy E (2.062e-03 J) + H (1.093e-05 J) = 2.073e-03 J\n",
" S[1][1] = +9.990e-01-4.099e-02i, |S[1][1]| = -1.509e-03, arg(S[1][1]) = -2.350e+00\n",
"\n",
"It 38/101: ω/2π = 3.185e+00 GHz (total elapsed time = 6.05e+00 s)\n",
"\n",
" Sol. ||E|| = 6.023575e+00\n",
" Field energy E (2.063e-03 J) + H (1.096e-05 J) = 2.073e-03 J\n",
" S[1][1] = +9.990e-01-4.106e-02i, |S[1][1]| = -1.513e-03, arg(S[1][1]) = -2.353e+00\n",
"\n",
"It 39/101: ω/2π = 3.190e+00 GHz (total elapsed time = 6.05e+00 s)\n",
"\n",
" Sol. ||E|| = 6.023661e+00\n",
" Field energy E (2.063e-03 J) + H (1.100e-05 J) = 2.074e-03 J\n",
" S[1][1] = +9.990e-01-4.112e-02i, |S[1][1]| = -1.518e-03, arg(S[1][1]) = -2.357e+00\n",
"\n",
"It 40/101: ω/2π = 3.195e+00 GHz (total elapsed time = 6.06e+00 s)\n",
"\n",
" Sol. ||E|| = 6.023748e+00\n",
" Field energy E (2.063e-03 J) + H (1.103e-05 J) = 2.074e-03 J\n",
" S[1][1] = +9.990e-01-4.119e-02i, |S[1][1]| = -1.522e-03, arg(S[1][1]) = -2.361e+00\n",
"\n",
"It 41/101: ω/2π = 3.200e+00 GHz (total elapsed time = 6.06e+00 s)\n",
"\n",
" Sol. ||E|| = 6.023834e+00\n",
" Field energy E (2.063e-03 J) + H (1.107e-05 J) = 2.074e-03 J\n",
" S[1][1] = +9.990e-01-4.125e-02i, |S[1][1]| = -1.526e-03, arg(S[1][1]) = -2.365e+00\n",
"\n",
"It 42/101: ω/2π = 3.205e+00 GHz (total elapsed time = 6.07e+00 s)\n",
"\n",
" Sol. ||E|| = 6.023921e+00\n",
" Field energy E (2.063e-03 J) + H (1.110e-05 J) = 2.074e-03 J\n",
" S[1][1] = +9.990e-01-4.132e-02i, |S[1][1]| = -1.531e-03, arg(S[1][1]) = -2.368e+00\n",
"\n",
"It 43/101: ω/2π = 3.210e+00 GHz (total elapsed time = 6.08e+00 s)\n",
"\n",
" Sol. ||E|| = 6.024008e+00\n",
" Field energy E (2.063e-03 J) + H (1.114e-05 J) = 2.074e-03 J\n",
" S[1][1] = +9.990e-01-4.138e-02i, |S[1][1]| = -1.535e-03, arg(S[1][1]) = -2.372e+00\n",
"\n",
"It 44/101: ω/2π = 3.215e+00 GHz (total elapsed time = 6.08e+00 s)\n",
"\n",
" Sol. ||E|| = 6.024095e+00\n",
" Field energy E (2.063e-03 J) + H (1.118e-05 J) = 2.074e-03 J\n",
" S[1][1] = +9.990e-01-4.145e-02i, |S[1][1]| = -1.540e-03, arg(S[1][1]) = -2.376e+00\n",
"\n",
"It 45/101: ω/2π = 3.220e+00 GHz (total elapsed time = 6.09e+00 s)\n",
"\n",
" Sol. ||E|| = 6.024182e+00\n",
" Field energy E (2.063e-03 J) + H (1.121e-05 J) = 2.074e-03 J\n",
" S[1][1] = +9.990e-01-4.151e-02i, |S[1][1]| = -1.544e-03, arg(S[1][1]) = -2.380e+00\n",
"\n",
"It 46/101: ω/2π = 3.225e+00 GHz (total elapsed time = 6.09e+00 s)\n",
"\n",
" Sol. ||E|| = 6.024269e+00\n",
" Field energy E (2.063e-03 J) + H (1.125e-05 J) = 2.074e-03 J\n",
" S[1][1] = +9.990e-01-4.158e-02i, |S[1][1]| = -1.548e-03, arg(S[1][1]) = -2.383e+00\n",
"\n",
"It 47/101: ω/2π = 3.230e+00 GHz (total elapsed time = 6.10e+00 s)\n",
"\n",
" Sol. ||E|| = 6.024357e+00\n",
" Field energy E (2.063e-03 J) + H (1.128e-05 J) = 2.074e-03 J\n",
" S[1][1] = +9.990e-01-4.164e-02i, |S[1][1]| = -1.553e-03, arg(S[1][1]) = -2.387e+00\n",
"\n",
"It 48/101: ω/2π = 3.235e+00 GHz (total elapsed time = 6.10e+00 s)\n",
"\n",
" Sol. ||E|| = 6.024444e+00\n",
" Field energy E (2.063e-03 J) + H (1.132e-05 J) = 2.074e-03 J\n",
" S[1][1] = +9.990e-01-4.171e-02i, |S[1][1]| = -1.557e-03, arg(S[1][1]) = -2.391e+00\n",
"\n",
"It 49/101: ω/2π = 3.240e+00 GHz (total elapsed time = 6.11e+00 s)\n",
"\n",
" Sol. ||E|| = 6.024532e+00\n",
" Field energy E (2.063e-03 J) + H (1.135e-05 J) = 2.075e-03 J\n",
" S[1][1] = +9.989e-01-4.177e-02i, |S[1][1]| = -1.562e-03, arg(S[1][1]) = -2.394e+00\n",
"\n",
"It 50/101: ω/2π = 3.245e+00 GHz (total elapsed time = 6.11e+00 s)\n",
"\n",
" Sol. ||E|| = 6.024620e+00\n",
" Field energy E (2.063e-03 J) + H (1.139e-05 J) = 2.075e-03 J\n",
" S[1][1] = +9.989e-01-4.184e-02i, |S[1][1]| = -1.566e-03, arg(S[1][1]) = -2.398e+00\n",
"\n",
"It 51/101: ω/2π = 3.250e+00 GHz (total elapsed time = 6.12e+00 s)\n",
"\n",
" Sol. ||E|| = 6.024707e+00\n",
" Field energy E (2.063e-03 J) + H (1.142e-05 J) = 2.075e-03 J\n",
" S[1][1] = +9.989e-01-4.190e-02i, |S[1][1]| = -1.570e-03, arg(S[1][1]) = -2.402e+00\n",
"\n",
"It 52/101: ω/2π = 3.255e+00 GHz (total elapsed time = 6.12e+00 s)\n",
"\n",
" Sol. ||E|| = 6.024796e+00\n",
" Field energy E (2.063e-03 J) + H (1.146e-05 J) = 2.075e-03 J\n",
" S[1][1] = +9.989e-01-4.197e-02i, |S[1][1]| = -1.575e-03, arg(S[1][1]) = -2.406e+00\n",
"\n",
"It 53/101: ω/2π = 3.260e+00 GHz (total elapsed time = 6.13e+00 s)\n",
"\n",
" Sol. ||E|| = 6.024884e+00\n",
" Field energy E (2.064e-03 J) + H (1.149e-05 J) = 2.075e-03 J\n",
" S[1][1] = +9.989e-01-4.203e-02i, |S[1][1]| = -1.579e-03, arg(S[1][1]) = -2.409e+00\n",
"\n",
"It 54/101: ω/2π = 3.265e+00 GHz (total elapsed time = 6.13e+00 s)\n",
"\n",
" Sol. ||E|| = 6.024972e+00\n",
" Field energy E (2.064e-03 J) + H (1.153e-05 J) = 2.075e-03 J\n",
" S[1][1] = +9.989e-01-4.210e-02i, |S[1][1]| = -1.584e-03, arg(S[1][1]) = -2.413e+00\n",
"\n",
"It 55/101: ω/2π = 3.270e+00 GHz (total elapsed time = 6.14e+00 s)\n",
"\n",
" Sol. ||E|| = 6.025061e+00\n",
" Field energy E (2.064e-03 J) + H (1.157e-05 J) = 2.075e-03 J\n",
" S[1][1] = +9.989e-01-4.216e-02i, |S[1][1]| = -1.588e-03, arg(S[1][1]) = -2.417e+00\n",
"\n",
"It 56/101: ω/2π = 3.275e+00 GHz (total elapsed time = 6.14e+00 s)\n",
"\n",
" Sol. ||E|| = 6.025149e+00\n",
" Field energy E (2.064e-03 J) + H (1.160e-05 J) = 2.075e-03 J\n",
" S[1][1] = +9.989e-01-4.223e-02i, |S[1][1]| = -1.593e-03, arg(S[1][1]) = -2.421e+00\n",
"\n",
"It 57/101: ω/2π = 3.280e+00 GHz (total elapsed time = 6.15e+00 s)\n",
"\n",
" Sol. ||E|| = 6.025238e+00\n",
" Field energy E (2.064e-03 J) + H (1.164e-05 J) = 2.075e-03 J\n",
" S[1][1] = +9.989e-01-4.229e-02i, |S[1][1]| = -1.597e-03, arg(S[1][1]) = -2.424e+00\n",
"\n",
"It 58/101: ω/2π = 3.285e+00 GHz (total elapsed time = 6.15e+00 s)\n",
"\n",
" Sol. ||E|| = 6.025327e+00\n",
" Field energy E (2.064e-03 J) + H (1.167e-05 J) = 2.076e-03 J\n",
" S[1][1] = +9.989e-01-4.236e-02i, |S[1][1]| = -1.602e-03, arg(S[1][1]) = -2.428e+00\n",
"\n",
"It 59/101: ω/2π = 3.290e+00 GHz (total elapsed time = 6.16e+00 s)\n",
"\n",
" Sol. ||E|| = 6.025416e+00\n",
" Field energy E (2.064e-03 J) + H (1.171e-05 J) = 2.076e-03 J\n",
" S[1][1] = +9.989e-01-4.242e-02i, |S[1][1]| = -1.606e-03, arg(S[1][1]) = -2.432e+00\n",
"\n",
"It 60/101: ω/2π = 3.295e+00 GHz (total elapsed time = 6.16e+00 s)\n",
"\n",
" Sol. ||E|| = 6.025505e+00\n",
" Field energy E (2.064e-03 J) + H (1.175e-05 J) = 2.076e-03 J\n",
" S[1][1] = +9.989e-01-4.249e-02i, |S[1][1]| = -1.611e-03, arg(S[1][1]) = -2.436e+00\n",
"\n",
"It 61/101: ω/2π = 3.300e+00 GHz (total elapsed time = 6.17e+00 s)\n",
"\n",
" Sol. ||E|| = 6.025595e+00\n",
" Field energy E (2.064e-03 J) + H (1.178e-05 J) = 2.076e-03 J\n",
" S[1][1] = +9.989e-01-4.255e-02i, |S[1][1]| = -1.615e-03, arg(S[1][1]) = -2.439e+00\n",
"\n",
"It 62/101: ω/2π = 3.305e+00 GHz (total elapsed time = 6.17e+00 s)\n",
"\n",
" Sol. ||E|| = 6.025684e+00\n",
" Field energy E (2.064e-03 J) + H (1.182e-05 J) = 2.076e-03 J\n",
" S[1][1] = +9.989e-01-4.262e-02i, |S[1][1]| = -1.620e-03, arg(S[1][1]) = -2.443e+00\n",
"\n",
"It 63/101: ω/2π = 3.310e+00 GHz (total elapsed time = 6.18e+00 s)\n",
"\n",
" Sol. ||E|| = 6.025774e+00\n",
" Field energy E (2.064e-03 J) + H (1.185e-05 J) = 2.076e-03 J\n",
" S[1][1] = +9.989e-01-4.268e-02i, |S[1][1]| = -1.624e-03, arg(S[1][1]) = -2.447e+00\n",
"\n",
"It 64/101: ω/2π = 3.315e+00 GHz (total elapsed time = 6.18e+00 s)\n",
"\n",
" Sol. ||E|| = 6.025863e+00\n",
" Field energy E (2.064e-03 J) + H (1.189e-05 J) = 2.076e-03 J\n",
" S[1][1] = +9.989e-01-4.275e-02i, |S[1][1]| = -1.629e-03, arg(S[1][1]) = -2.450e+00\n",
"\n",
"It 65/101: ω/2π = 3.320e+00 GHz (total elapsed time = 6.19e+00 s)\n",
"\n",
" Sol. ||E|| = 6.025953e+00\n",
" Field energy E (2.064e-03 J) + H (1.193e-05 J) = 2.076e-03 J\n",
" S[1][1] = +9.989e-01-4.281e-02i, |S[1][1]| = -1.633e-03, arg(S[1][1]) = -2.454e+00\n",
"\n",
"It 66/101: ω/2π = 3.325e+00 GHz (total elapsed time = 6.19e+00 s)\n",
"\n",
" Sol. ||E|| = 6.026043e+00\n",
" Field energy E (2.064e-03 J) + H (1.196e-05 J) = 2.076e-03 J\n",
" S[1][1] = +9.989e-01-4.288e-02i, |S[1][1]| = -1.638e-03, arg(S[1][1]) = -2.458e+00\n",
"\n",
"It 67/101: ω/2π = 3.330e+00 GHz (total elapsed time = 6.20e+00 s)\n",
"\n",
" Sol. ||E|| = 6.026134e+00\n",
" Field energy E (2.064e-03 J) + H (1.200e-05 J) = 2.076e-03 J\n",
" S[1][1] = +9.989e-01-4.294e-02i, |S[1][1]| = -1.642e-03, arg(S[1][1]) = -2.462e+00\n",
"\n",
"It 68/101: ω/2π = 3.335e+00 GHz (total elapsed time = 6.21e+00 s)\n",
"\n",
" Sol. ||E|| = 6.026224e+00\n",
" Field energy E (2.065e-03 J) + H (1.204e-05 J) = 2.077e-03 J\n",
" S[1][1] = +9.989e-01-4.301e-02i, |S[1][1]| = -1.647e-03, arg(S[1][1]) = -2.465e+00\n",
"\n",
"It 69/101: ω/2π = 3.340e+00 GHz (total elapsed time = 6.21e+00 s)\n",
"\n",
" Sol. ||E|| = 6.026314e+00\n",
" Field energy E (2.065e-03 J) + H (1.207e-05 J) = 2.077e-03 J\n",
" S[1][1] = +9.989e-01-4.307e-02i, |S[1][1]| = -1.651e-03, arg(S[1][1]) = -2.469e+00\n",
"\n",
"It 70/101: ω/2π = 3.345e+00 GHz (total elapsed time = 6.22e+00 s)\n",
"\n",
" Sol. ||E|| = 6.026405e+00\n",
" Field energy E (2.065e-03 J) + H (1.211e-05 J) = 2.077e-03 J\n",
" S[1][1] = +9.989e-01-4.314e-02i, |S[1][1]| = -1.656e-03, arg(S[1][1]) = -2.473e+00\n",
"\n",
"It 71/101: ω/2π = 3.350e+00 GHz (total elapsed time = 6.22e+00 s)\n",
"\n",
" Sol. ||E|| = 6.026496e+00\n",
" Field energy E (2.065e-03 J) + H (1.215e-05 J) = 2.077e-03 J\n",
" S[1][1] = +9.989e-01-4.320e-02i, |S[1][1]| = -1.660e-03, arg(S[1][1]) = -2.477e+00\n",
"\n",
"It 72/101: ω/2π = 3.355e+00 GHz (total elapsed time = 6.23e+00 s)\n",
"\n",
" Sol. ||E|| = 6.026587e+00\n",
" Field energy E (2.065e-03 J) + H (1.218e-05 J) = 2.077e-03 J\n",
" S[1][1] = +9.989e-01-4.327e-02i, |S[1][1]| = -1.665e-03, arg(S[1][1]) = -2.480e+00\n",
"\n",
"It 73/101: ω/2π = 3.360e+00 GHz (total elapsed time = 6.23e+00 s)\n",
"\n",
" Sol. ||E|| = 6.026678e+00\n",
" Field energy E (2.065e-03 J) + H (1.222e-05 J) = 2.077e-03 J\n",
" S[1][1] = +9.989e-01-4.333e-02i, |S[1][1]| = -1.669e-03, arg(S[1][1]) = -2.484e+00\n",
"\n",
"It 74/101: ω/2π = 3.365e+00 GHz (total elapsed time = 6.24e+00 s)\n",
"\n",
" Sol. ||E|| = 6.026769e+00\n",
" Field energy E (2.065e-03 J) + H (1.226e-05 J) = 2.077e-03 J\n",
" S[1][1] = +9.989e-01-4.340e-02i, |S[1][1]| = -1.674e-03, arg(S[1][1]) = -2.488e+00\n",
"\n",
"It 75/101: ω/2π = 3.370e+00 GHz (total elapsed time = 6.24e+00 s)\n",
"\n",
" Sol. ||E|| = 6.026860e+00\n",
" Field energy E (2.065e-03 J) + H (1.229e-05 J) = 2.077e-03 J\n",
" S[1][1] = +9.989e-01-4.346e-02i, |S[1][1]| = -1.679e-03, arg(S[1][1]) = -2.492e+00\n",
"\n",
"It 76/101: ω/2π = 3.375e+00 GHz (total elapsed time = 6.25e+00 s)\n",
"\n",
" Sol. ||E|| = 6.026951e+00\n",
" Field energy E (2.065e-03 J) + H (1.233e-05 J) = 2.077e-03 J\n",
" S[1][1] = +9.989e-01-4.353e-02i, |S[1][1]| = -1.683e-03, arg(S[1][1]) = -2.495e+00\n",
"\n",
"It 77/101: ω/2π = 3.380e+00 GHz (total elapsed time = 6.25e+00 s)\n",
"\n",
" Sol. ||E|| = 6.027043e+00\n",
" Field energy E (2.065e-03 J) + H (1.237e-05 J) = 2.078e-03 J\n",
" S[1][1] = +9.989e-01-4.360e-02i, |S[1][1]| = -1.688e-03, arg(S[1][1]) = -2.499e+00\n",
"\n",
"It 78/101: ω/2π = 3.385e+00 GHz (total elapsed time = 6.26e+00 s)\n",
"\n",
" Sol. ||E|| = 6.027135e+00\n",
" Field energy E (2.065e-03 J) + H (1.241e-05 J) = 2.078e-03 J\n",
" S[1][1] = +9.989e-01-4.366e-02i, |S[1][1]| = -1.692e-03, arg(S[1][1]) = -2.503e+00\n",
"\n",
"It 79/101: ω/2π = 3.390e+00 GHz (total elapsed time = 6.27e+00 s)\n",
"\n",
" Sol. ||E|| = 6.027227e+00\n",
" Field energy E (2.065e-03 J) + H (1.244e-05 J) = 2.078e-03 J\n",
" S[1][1] = +9.988e-01-4.373e-02i, |S[1][1]| = -1.697e-03, arg(S[1][1]) = -2.507e+00\n",
"\n",
"It 80/101: ω/2π = 3.395e+00 GHz (total elapsed time = 6.27e+00 s)\n",
"\n",
" Sol. ||E|| = 6.027319e+00\n",
" Field energy E (2.065e-03 J) + H (1.248e-05 J) = 2.078e-03 J\n",
" S[1][1] = +9.988e-01-4.379e-02i, |S[1][1]| = -1.702e-03, arg(S[1][1]) = -2.510e+00\n",
"\n",
"It 81/101: ω/2π = 3.400e+00 GHz (total elapsed time = 6.28e+00 s)\n",
"\n",
" Sol. ||E|| = 6.027411e+00\n",
" Field energy E (2.065e-03 J) + H (1.252e-05 J) = 2.078e-03 J\n",
" S[1][1] = +9.988e-01-4.386e-02i, |S[1][1]| = -1.706e-03, arg(S[1][1]) = -2.514e+00\n",
"\n",
"It 82/101: ω/2π = 3.405e+00 GHz (total elapsed time = 6.28e+00 s)\n",
"\n",
" Sol. ||E|| = 6.027503e+00\n",
" Field energy E (2.065e-03 J) + H (1.255e-05 J) = 2.078e-03 J\n",
" S[1][1] = +9.988e-01-4.392e-02i, |S[1][1]| = -1.711e-03, arg(S[1][1]) = -2.518e+00\n",
"\n",
"It 83/101: ω/2π = 3.410e+00 GHz (total elapsed time = 6.29e+00 s)\n",
"\n",
" Sol. ||E|| = 6.027595e+00\n",
" Field energy E (2.066e-03 J) + H (1.259e-05 J) = 2.078e-03 J\n",
" S[1][1] = +9.988e-01-4.399e-02i, |S[1][1]| = -1.715e-03, arg(S[1][1]) = -2.522e+00\n",
"\n",
"It 84/101: ω/2π = 3.415e+00 GHz (total elapsed time = 6.30e+00 s)\n",
"\n",
" Sol. ||E|| = 6.027688e+00\n",
" Field energy E (2.066e-03 J) + H (1.263e-05 J) = 2.078e-03 J\n",
" S[1][1] = +9.988e-01-4.405e-02i, |S[1][1]| = -1.720e-03, arg(S[1][1]) = -2.525e+00\n",
"\n",
"It 85/101: ω/2π = 3.420e+00 GHz (total elapsed time = 6.30e+00 s)\n",
"\n",
" Sol. ||E|| = 6.027781e+00\n",
" Field energy E (2.066e-03 J) + H (1.267e-05 J) = 2.078e-03 J\n",
" S[1][1] = +9.988e-01-4.412e-02i, |S[1][1]| = -1.725e-03, arg(S[1][1]) = -2.529e+00\n",
"\n",
"It 86/101: ω/2π = 3.425e+00 GHz (total elapsed time = 6.31e+00 s)\n",
"\n",
" Sol. ||E|| = 6.027873e+00\n",
" Field energy E (2.066e-03 J) + H (1.270e-05 J) = 2.078e-03 J\n",
" S[1][1] = +9.988e-01-4.418e-02i, |S[1][1]| = -1.729e-03, arg(S[1][1]) = -2.533e+00\n",
"\n",
"It 87/101: ω/2π = 3.430e+00 GHz (total elapsed time = 6.31e+00 s)\n",
"\n",
" Sol. ||E|| = 6.027966e+00\n",
" Field energy E (2.066e-03 J) + H (1.274e-05 J) = 2.079e-03 J\n",
" S[1][1] = +9.988e-01-4.425e-02i, |S[1][1]| = -1.734e-03, arg(S[1][1]) = -2.537e+00\n",
"\n",
"It 88/101: ω/2π = 3.435e+00 GHz (total elapsed time = 6.32e+00 s)\n",
"\n",
" Sol. ||E|| = 6.028059e+00\n",
" Field energy E (2.066e-03 J) + H (1.278e-05 J) = 2.079e-03 J\n",
" S[1][1] = +9.988e-01-4.431e-02i, |S[1][1]| = -1.739e-03, arg(S[1][1]) = -2.540e+00\n",
"\n",
"It 89/101: ω/2π = 3.440e+00 GHz (total elapsed time = 6.32e+00 s)\n",
"\n",
" Sol. ||E|| = 6.028153e+00\n",
" Field energy E (2.066e-03 J) + H (1.282e-05 J) = 2.079e-03 J\n",
" S[1][1] = +9.988e-01-4.438e-02i, |S[1][1]| = -1.743e-03, arg(S[1][1]) = -2.544e+00\n",
"\n",
"It 90/101: ω/2π = 3.445e+00 GHz (total elapsed time = 6.33e+00 s)\n",
"\n",
" Sol. ||E|| = 6.028246e+00\n",
" Field energy E (2.066e-03 J) + H (1.286e-05 J) = 2.079e-03 J\n",
" S[1][1] = +9.988e-01-4.444e-02i, |S[1][1]| = -1.748e-03, arg(S[1][1]) = -2.548e+00\n",
"\n",
"It 91/101: ω/2π = 3.450e+00 GHz (total elapsed time = 6.34e+00 s)\n",
"\n",
" Sol. ||E|| = 6.028340e+00\n",
" Field energy E (2.066e-03 J) + H (1.289e-05 J) = 2.079e-03 J\n",
" S[1][1] = +9.988e-01-4.451e-02i, |S[1][1]| = -1.753e-03, arg(S[1][1]) = -2.551e+00\n",
"\n",
"It 92/101: ω/2π = 3.455e+00 GHz (total elapsed time = 6.34e+00 s)\n",
"\n",
" Sol. ||E|| = 6.028433e+00\n",
" Field energy E (2.066e-03 J) + H (1.293e-05 J) = 2.079e-03 J\n",
" S[1][1] = +9.988e-01-4.457e-02i, |S[1][1]| = -1.758e-03, arg(S[1][1]) = -2.555e+00\n",
"\n",
"It 93/101: ω/2π = 3.460e+00 GHz (total elapsed time = 6.35e+00 s)\n",
"\n",
" Sol. ||E|| = 6.028527e+00\n",
" Field energy E (2.066e-03 J) + H (1.297e-05 J) = 2.079e-03 J\n",
" S[1][1] = +9.988e-01-4.464e-02i, |S[1][1]| = -1.762e-03, arg(S[1][1]) = -2.559e+00\n",
"\n",
"It 94/101: ω/2π = 3.465e+00 GHz (total elapsed time = 6.35e+00 s)\n",
"\n",
" Sol. ||E|| = 6.028621e+00\n",
" Field energy E (2.066e-03 J) + H (1.301e-05 J) = 2.079e-03 J\n",
" S[1][1] = +9.988e-01-4.470e-02i, |S[1][1]| = -1.767e-03, arg(S[1][1]) = -2.563e+00\n",
"\n",
"It 95/101: ω/2π = 3.470e+00 GHz (total elapsed time = 6.36e+00 s)\n",
"\n",
" Sol. ||E|| = 6.028715e+00\n",
" Field energy E (2.066e-03 J) + H (1.305e-05 J) = 2.079e-03 J\n",
" S[1][1] = +9.988e-01-4.477e-02i, |S[1][1]| = -1.772e-03, arg(S[1][1]) = -2.566e+00\n",
"\n",
"It 96/101: ω/2π = 3.475e+00 GHz (total elapsed time = 6.36e+00 s)\n",
"\n",
" Sol. ||E|| = 6.028809e+00\n",
" Field energy E (2.066e-03 J) + H (1.308e-05 J) = 2.080e-03 J\n",
" S[1][1] = +9.988e-01-4.483e-02i, |S[1][1]| = -1.776e-03, arg(S[1][1]) = -2.570e+00\n",
"\n",
"It 97/101: ω/2π = 3.480e+00 GHz (total elapsed time = 6.37e+00 s)\n",
"\n",
" Sol. ||E|| = 6.028904e+00\n",
" Field energy E (2.067e-03 J) + H (1.312e-05 J) = 2.080e-03 J\n",
" S[1][1] = +9.988e-01-4.490e-02i, |S[1][1]| = -1.781e-03, arg(S[1][1]) = -2.574e+00\n",
"\n",
"It 98/101: ω/2π = 3.485e+00 GHz (total elapsed time = 6.37e+00 s)\n",
"\n",
" Sol. ||E|| = 6.028998e+00\n",
" Field energy E (2.067e-03 J) + H (1.316e-05 J) = 2.080e-03 J\n",
" S[1][1] = +9.988e-01-4.496e-02i, |S[1][1]| = -1.786e-03, arg(S[1][1]) = -2.578e+00\n",
"\n",
"It 99/101: ω/2π = 3.490e+00 GHz (total elapsed time = 6.38e+00 s)\n",
"\n",
" Sol. ||E|| = 6.029093e+00\n",
" Field energy E (2.067e-03 J) + H (1.320e-05 J) = 2.080e-03 J\n",
" S[1][1] = +9.988e-01-4.503e-02i, |S[1][1]| = -1.791e-03, arg(S[1][1]) = -2.581e+00\n",
"\n",
"It 100/101: ω/2π = 3.495e+00 GHz (total elapsed time = 6.38e+00 s)\n",
"\n",
" Sol. ||E|| = 6.029188e+00\n",
" Field energy E (2.067e-03 J) + H (1.324e-05 J) = 2.080e-03 J\n",
" S[1][1] = +9.988e-01-4.510e-02i, |S[1][1]| = -1.795e-03, arg(S[1][1]) = -2.585e+00\n",
"\n",
"It 101/101: ω/2π = 3.500e+00 GHz (total elapsed time = 6.39e+00 s)\n",
"\n",
" Sol. ||E|| = 6.029283e+00\n",
" Field energy E (2.067e-03 J) + H (1.328e-05 J) = 2.080e-03 J\n",
" S[1][1] = +9.988e-01-4.516e-02i, |S[1][1]| = -1.800e-03, arg(S[1][1]) = -2.589e+00\n",
"\n",
"Completed 0 iterations of adaptive mesh refinement (AMR):\n",
" Indicator norm = 1.881e-01, global unknowns = 49288\n",
" Max. iterations = 0, tol. = 1.000e-02\n",
"\n",
"Elapsed Time Report (s) Min. Max. Avg.\n",
"==============================================================\n",
"Initialization 0.031 0.032 0.032\n",
" Mesh Preprocessing 0.098 0.099 0.099\n",
"Operator Construction 0.054 0.058 0.057\n",
"Linear Solve 0.228 0.240 0.232\n",
" Setup 1.490 1.491 1.490\n",
" Preconditioner 2.479 2.534 2.512\n",
" Coarse Solve 0.926 0.971 0.944\n",
"PROM Construction 0.050 0.054 0.051\n",
"PROM Solve 0.010 0.032 0.029\n",
"Estimation 0.017 0.018 0.017\n",
" Construction 0.514 0.516 0.515\n",
" Solve 0.549 0.550 0.550\n",
"Postprocessing 0.549 0.571 0.552\n",
"Disk IO 0.775 0.775 0.775\n",
"--------------------------------------------------------------\n",
"Total 7.885 7.885 7.885\n",
"\n"
]
}
],
"source": [
"def attr(name):\n",
" return [pg_map[name]] if name in pg_map else []\n",
"\n",
"sim = Simulation(output_dir=os.getcwd(), apply_mesh_options=False)\n",
"sim.config = {\n",
" \"Problem\": {\n",
" \"Type\": \"Driven\",\n",
" \"Verbose\": 2,\n",
" \"Output\": \"postpro/sw_antenna\"\n",
" },\n",
"\n",
" \"Model\": {\n",
" \"Mesh\": filename,\n",
" \"L0\": 1.0,\n",
" \"Refinement\": {}\n",
" },\n",
"\n",
" \"Domains\": {\n",
" \"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",
"\n",
" \"Boundaries\": {\n",
" \"PEC\": {\n",
" \"Attributes\": attr(\"ground_plane\") + attr(\"patch\")\n",
" },\n",
"\n",
" \"LumpedPort\": [\n",
" {\n",
" \"Index\": 1,\n",
" \"Attributes\": attr(\"lumped_port\"),\n",
" \"R\": port_impedance,\n",
" \"Excitation\": True,\n",
" \"Direction\": \"+Z\"\n",
" }\n",
" ],\n",
"\n",
" \"Absorbing\": {\n",
" \"Attributes\": attr(\"farfield\"),\n",
" \"Order\": 1\n",
" }\n",
" },\n",
"\n",
" \"Solver\": {\n",
" \"Order\": solver_order,\n",
" \"Device\": \"CPU\",\n",
"\n",
" \"Driven\": {\n",
" \"MinFreq\": freq_min,\n",
" \"MaxFreq\": freq_max,\n",
" \"FreqStep\": freq_step,\n",
" \"AdaptiveTol\": 0.001\n",
" },\n",
"\n",
" \"Linear\": {\n",
" \"Type\": \"Default\",\n",
" \"KSPType\": \"GMRES\",\n",
" \"Tol\": 1.0e-8,\n",
" \"MaxIts\": 200,\n",
" \"ComplexCoarseSolve\": True\n",
" }\n",
" }\n",
"}\n",
"\n",
"config_path = str(sim.write_config(output_file))\n",
"run_palace(config_path, num_procs=8, work_dir=os.getcwd())"
]
}
],
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"language": "python",
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"duration": 7.135765,
"end_time": "2026-05-27T20:02:17.692958+00:00",
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"exception": null,
"input_path": "docs/examples/step_in_width.ipynb",
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"start_time": "2026-05-27T20:02:10.557193+00:00",
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