Dipole Antenna Mesh with PalaceToolkit#
This notebook uses PalaceToolkit utilities with a robust workflow:
build primitives
fragment once for conformal topology
define
Entityobjects from fragmented geometryrun
run_meshing_pipeline, refine withrefine_near_surfaces, thengenerate_3d_meshvisualize with
palacetoolkit.viz
from pathlib import Path
import math
import gmsh
from palacetoolkit.geometry import xmin, xmax, ymin, ymax, zmin, zmax, extract_tag
from palacetoolkit.mesh import Entity, run_meshing_pipeline, generate_3d_mesh, refine_near_surfaces
from palacetoolkit.viz import view_mesh
from palacetoolkit.simulation import generate_palace_config_from_entities, run_palace
from palacetoolkit.verify_topology import verify, print_report, visualise_problems
wavelength = 4.0
arm_length = wavelength / 4
arm_radius = arm_length / 20
gap_size = arm_length / 50
outer_boundary_radius = 1.5 * wavelength
mesh_file = "dipole.msh"
if gmsh.isInitialized():
gmsh.finalize()
gmsh.initialize()
gmsh.option.setNumber("General.Verbosity", 2)
gmsh.model.add("dipole_entity_pipeline")
occ = gmsh.model.occ
air = occ.addSphere(0, 0, 0, outer_boundary_radius)
top_arm = occ.addBox(-arm_radius, -arm_radius, gap_size / 2, 2 * arm_radius, 2 * arm_radius, arm_length)
bot_arm = occ.addBox(-arm_radius, -arm_radius, -gap_size / 2 - arm_length, 2 * arm_radius, 2 * arm_radius, arm_length)
port_sheet = occ.addRectangle(-arm_radius, -gap_size / 2, 0, 2 * arm_radius, gap_size)
occ.rotate([(2, port_sheet)], 0, 0, 0, 1, 0, 0, math.pi / 2)
occ.synchronize()
# Entity + boolean pipeline for named physical groups.
entities = [
Entity("air", dim=3, mesh_order=2, btype="dielectric", tags=[air], loss_tan=0.0, eps_r=1.0, mu_r=1.0),
Entity("top_arm", dim=3, mesh_order=1, btype="pec", tags=[top_arm]),
Entity("bot_arm", dim=3, mesh_order=1, btype="pec", tags=[bot_arm]),
Entity("port", dim=2, mesh_order=0, btype="lumped_port", tags=[port_sheet], R=50.0, direction="+Z", excitation=True),
]
pg_map = run_meshing_pipeline(entities)
refine_near_surfaces(
entities[2].dimtags,
wavelength,
ppw_near=30,
ppw_far=5,
transition_distance=wavelength / 4,
set_as_background=True
)
generate_3d_mesh(entities, output_file=mesh_file, optimize=True)
gmsh.finalize()
pg_map
Physical group 'air' (dim=3): pg=1, tags=[1]
Physical group 'top_arm' (dim=3): pg=2, tags=[2]
Physical group 'bot_arm' (dim=3): pg=3, tags=[3]
Physical group 'port' (dim=2): pg=4, tags=[14]
Physical group 'air__None' (dim=2): pg=5, tags=[23]
Physical group 'air__bot_arm' (dim=2): pg=6, tags=[19, 10, 21, 22, 11, 12, 20]
Physical group 'air__top_arm' (dim=2): pg=7, tags=[15, 4, 7, 5, 17, 18, 16]
ppw_near=30 ppw_far=5
SizeMax=0.8000 transition=1.0000
global: 7 curves, SizeMin=0.1333
Warning : Unknown curve 11
Warning : Unknown curve 21
Warning : ------------------------------
Warning : Mesh generation error summary
Warning : 2 warnings
Warning : 0 errors
Warning : Check the full log for details
Warning : ------------------------------
Mesh saved to dipole.msh
Nodes: 1994
Elements: 10919
{'port': 4,
'air__None': 5,
'air__bot_arm': 6,
'air__top_arm': 7,
'air': 1,
'top_arm': 2,
'bot_arm': 3}
view_mesh(mesh_file, transparent_groups=["air__None"])
Loading mesh file: dipole.msh
Groups to render transparent: ['air__None']
Mesh loaded successfully with 2 cell blocks
Found 2006 triangles total
Physical group tags in mesh: {4: 'port', 5: 'air__None', 6: 'air__bot_arm', 7: 'air__top_arm'}
config_file: str = "dipole_antenna.json"
mesh_file = "dipole.msh"
# Frequency sweep centered around the dipole resonance.
# Each arm is lambda/4, so total dipole length is lambda/2 and
# the resonant frequency is approximately f0 = c / lambda.
c0 = 299_792_458.0
f0_hz = c0 / wavelength
f0_ghz = f0_hz / 1e9
freq_min: float = 0.75 * f0_ghz
freq_max: float = 1.25 * f0_ghz
freq_step: float = (freq_max-freq_min)/20
solver_order: int = 2
print(f"Estimated f0 = {f0_ghz:.6f} GHz")
print(f"Sweep: {freq_min:.6f} to {freq_max:.6f} GHz (step {freq_step:.6f} GHz)")
generate_palace_config_from_entities(entity_defs = [e.to_dict() for e in entities],
pg_map = pg_map,
mesh_file = mesh_file,
output_file = config_file,
freq_min = freq_min,
freq_max = freq_max,
freq_step = freq_step ,
L0 = 1.0,
solver_order = solver_order,
absorbing_order = 2,
farfield=True)
Estimated f0 = 0.074948 GHz
Sweep: 0.056211 to 0.093685 GHz (step 0.001874 GHz)
Palace config written to dipole_antenna.json
{'Problem': {'Type': 'Driven',
'Verbose': 2,
'Output': 'postpro/dipole_antenna'},
'Model': {'Mesh': 'dipole.msh', 'L0': 1.0, 'Refinement': {}},
'Domains': {'Materials': [{'Attributes': [1],
'Permeability': 1.0,
'Permittivity': 1.0,
'LossTan': 0.0}]},
'Boundaries': {'PEC': {'Attributes': [2, 3]},
'Absorbing': {'Attributes': [5, 6, 7], 'Order': 2},
'LumpedPort': [{'Index': 1,
'Attributes': [4],
'R': 50.0,
'Excitation': True,
'Direction': '+Z'}],
'Postprocessing': {'FarField': {'Attributes': [5, 6, 7], 'NSample': 16000}}},
'Solver': {'Order': 2,
'Device': 'CPU',
'Driven': {'MinFreq': 0.056211085875,
'MaxFreq': 0.093685143125,
'FreqStep': 0.0018737028625,
'SaveStep': 5,
'AdaptiveTol': 0.001},
'Linear': {'Type': 'Default',
'KSPType': 'GMRES',
'Tol': 1e-08,
'MaxIts': 500}}}
# Validate topology before launching Palace.
topology_result = verify(mesh_file, config_file)
topology_ok = print_report(topology_result)
if not topology_ok:
print("Topology validation failed; opening mesh viewer in debug mode (problem faces highlighted).")
visualise_problems(
mesh_file,
topology_result,
transparent_groups=["air__None"],
exclude_expected_periodic=False,
only_nonmanifold=False,
)
raise RuntimeError("Mesh topology validation failed. Fix mesh/topology issues before running Palace.")
╔══════════════════════════════════════════════════════════════════════╗
║ Mesh Topological Consistency Report ║
╚══════════════════════════════════════════════════════════════════════╝
Mesh file: dipole.msh
Vertices: 1,994
Tetrahedra: 8,791
Boundary triangles: 2,006
Unique volume faces: 18,519
interior (2 tets): 16,645
skin (1 tet): 1,874
Physical groups (2-D):
attr 1 = air
attr 2 = top_arm
attr 3 = bot_arm
attr 4 = port
attr 5 = air__None
attr 6 = air__bot_arm
attr 7 = air__top_arm
──────────────────────────────────────────────────────────────────────
CHECK 1 — Totality: every boundary face ∈ volume faces
(violation → MFEM abort: (r,c,f) = …)
──────────────────────────────────────────────────────────────────────
✅ Pass 1 (raw): all boundary faces found among volume faces.
ⓘ Pass 2 (periodic): skipped — no periodic BC.
──────────────────────────────────────────────────────────────────────
CHECK 2 — Injectivity: each volume face has ≤ 1 boundary element
(violation → "…cannot have multiple boundary elements!")
──────────────────────────────────────────────────────────────────────
✅ Pass 1 (raw): no duplicate boundary faces.
ⓘ Pass 2 (periodic): skipped — no periodic BC.
──────────────────────────────────────────────────────────────────────
CHECK 3 — Volume manifoldness: each volume face has <= 2 tets
(violation → MFEM: "Interior triangular face found …")
──────────────────────────────────────────────────────────────────────
✅ Pass 1 (raw): no non-manifold volume faces.
ⓘ Pass 2 (periodic): skipped — no periodic BC.
──────────────────────────────────────────────────────────────────────
✅ RESULT: Mesh passes both topological checks.
──────────────────────────────────────────────────────────────────────
run_palace(config_file=config_file, num_procs=16)
Running: apptainer exec --pwd /work --bind /home/martin/Desktop/PalaceToolkit/docs/examples:/work /opt/palace/Palace.sif mpirun -np 16 /opt/palace/bin/palace-x86_64.bin /work/dipole_antenna.json
_____________ _______
_____ __ \____ __ /____ ____________
____ /_/ / __ ` / / __ ` / ___/ _ \
___ _____/ /_/ / / /_/ / /__/ ___/
/__/ \___,__/__/\___,__/\_____\_____/
--> Warning!
Output folder is not empty; program will overwrite content! (postpro/dipole_antenna)
Git changeset ID: v0.14.0-270-g9d6ea72f
Running with 16 MPI processes, 1 OpenMP thread
Device configuration: omp,cpu
Memory configuration: host-std
libCEED backend: /cpu/self/xsmm/blocked
Removed 204 unmarked domain elements from the mesh
Finished partitioning mesh into 16 subdomains
Characteristic length and time scales:
L₀ = 1.200e+01 m, t₀ = 4.003e+01 ns
Mesh curvature order: 1
Mesh bounding box:
(Xmin, Ymin, Zmin) = (-5.987e+00, -5.993e+00, -6.000e+00) m
(Xmax, Ymax, Zmax) = (+6.000e+00, +5.991e+00, +6.000e+00) m
Parallel Mesh Stats:
minimum average maximum total
vertices 85 123 181 1974
edges 609 722 856 11560
faces 1056 1136 1202 18176
elements 523 536 552 8587
neighbors 6 8 15
minimum maximum
h 0.00323682 0.1219
kappa 1.10887 8.33158
--> Warning!
Unknown PEC boundary attributes!
Solver will just ignore them!
Boundary attribute list: 2-3
Configuring Robin absorbing BC (order 2) at attributes:
5-7
Configuring Robin impedance BC for lumped ports at attributes:
4: Rs = 2.500e+02 Ω/sq, n = (+0.0,-1.0,+0.0)
Configuring lumped port circuit properties:
Index = 1: R = 5.000e+01 Ω
Configuring lumped port excitation source term at attributes:
4: Index = 1
Computing adaptive fast frequency response for:
Excitation with index 1 has contributions from:
Lumped port 1
Beginning PROM construction offline phase:
21 points for frequency sweep over [5.621e-02, 9.369e-02] GHz
Assembling system matrices, number of global unknowns:
H1 (p = 2): 13534, ND (p = 2): 59472, RT (p = 2): 80289
Operator assembly level: Partial
Mesh geometries:
Tetrahedron: P = 20, Q = 11 (quadrature order = 4)
Assembling multigrid hierarchy:
Level 0 (p = 1): 11560 unknowns
Level 1 (p = 2): 59472 unknowns
Level 0 (auxiliary) (p = 1): 1974 unknowns
Level 1 (auxiliary) (p = 2): 13534 unknowns
Residual norms for GMRES solve
0 (restart 0) KSP residual norm 1.838179e+01
1 (restart 0) KSP residual norm 1.820537e+01
2 (restart 0) KSP residual norm 1.764846e+01
3 (restart 0) KSP residual norm 1.751396e+01
4 (restart 0) KSP residual norm 1.729224e+01
5 (restart 0) KSP residual norm 1.388227e+01
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7 (restart 0) KSP residual norm 5.806985e+00
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10 (restart 0) KSP residual norm 4.988094e+00
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14 (restart 0) KSP residual norm 3.952913e+00
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68 (restart 0) KSP residual norm 9.104768e-03
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100 (restart 0) KSP residual norm 4.626108e-05
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105 (restart 0) KSP residual norm 1.821356e-05
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107 (restart 0) KSP residual norm 1.270711e-05
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127 (restart 0) KSP residual norm 2.008116e-07
128 (restart 0) KSP residual norm 1.751650e-07
GMRES solver converged in 128 iterations (avg. reduction factor: 8.656e-01)
Field energy E (8.510e-01 J) + H (7.806e-02 J) = 9.290e-01 J
Residual norms for GMRES solve
0 (restart 0) KSP residual norm 6.910536e+01
1 (restart 0) KSP residual norm 5.140182e+01
2 (restart 0) KSP residual norm 5.079719e+01
3 (restart 0) KSP residual norm 3.876424e+01
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8 (restart 0) KSP residual norm 8.709881e+00
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10 (restart 0) KSP residual norm 5.037669e+00
11 (restart 0) KSP residual norm 4.771643e+00
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13 (restart 0) KSP residual norm 3.539946e+00
14 (restart 0) KSP residual norm 3.262797e+00
15 (restart 0) KSP residual norm 2.456810e+00
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98 (restart 0) KSP residual norm 1.237904e-04
99 (restart 0) KSP residual norm 1.074157e-04
100 (restart 0) KSP residual norm 8.825905e-05
101 (restart 0) KSP residual norm 7.540290e-05
102 (restart 0) KSP residual norm 6.448310e-05
103 (restart 0) KSP residual norm 5.587905e-05
104 (restart 0) KSP residual norm 4.873683e-05
105 (restart 0) KSP residual norm 4.088910e-05
106 (restart 0) KSP residual norm 3.541985e-05
107 (restart 0) KSP residual norm 3.004047e-05
108 (restart 0) KSP residual norm 2.531954e-05
109 (restart 0) KSP residual norm 2.195109e-05
110 (restart 0) KSP residual norm 1.897932e-05
111 (restart 0) KSP residual norm 1.656845e-05
112 (restart 0) KSP residual norm 1.418329e-05
113 (restart 0) KSP residual norm 1.229588e-05
114 (restart 0) KSP residual norm 1.067992e-05
115 (restart 0) KSP residual norm 9.272476e-06
116 (restart 0) KSP residual norm 8.044695e-06
117 (restart 0) KSP residual norm 6.874367e-06
118 (restart 0) KSP residual norm 5.659595e-06
119 (restart 0) KSP residual norm 4.832767e-06
120 (restart 0) KSP residual norm 3.956145e-06
121 (restart 0) KSP residual norm 3.254175e-06
122 (restart 0) KSP residual norm 2.722758e-06
123 (restart 0) KSP residual norm 2.273313e-06
124 (restart 0) KSP residual norm 1.938301e-06
125 (restart 0) KSP residual norm 1.617064e-06
126 (restart 0) KSP residual norm 1.342308e-06
127 (restart 0) KSP residual norm 1.127054e-06
128 (restart 0) KSP residual norm 9.265384e-07
129 (restart 0) KSP residual norm 7.502585e-07
130 (restart 0) KSP residual norm 6.246350e-07
GMRES solver converged in 130 iterations (avg. reduction factor: 8.672e-01)
Field energy E (6.429e-01 J) + H (9.762e-02 J) = 7.405e-01 J
Residual norms for GMRES solve
0 (restart 0) KSP residual norm 3.349400e+01
1 (restart 0) KSP residual norm 3.339599e+01
2 (restart 0) KSP residual norm 3.331788e+01
3 (restart 0) KSP residual norm 1.382389e+01
4 (restart 0) KSP residual norm 1.347580e+01
5 (restart 0) KSP residual norm 1.221700e+01
6 (restart 0) KSP residual norm 1.082680e+01
7 (restart 0) KSP residual norm 1.022810e+01
8 (restart 0) KSP residual norm 1.019635e+01
9 (restart 0) KSP residual norm 8.598836e+00
10 (restart 0) KSP residual norm 8.507451e+00
11 (restart 0) KSP residual norm 7.712787e+00
12 (restart 0) KSP residual norm 7.415415e+00
13 (restart 0) KSP residual norm 7.176818e+00
14 (restart 0) KSP residual norm 7.011953e+00
15 (restart 0) KSP residual norm 6.024465e+00
16 (restart 0) KSP residual norm 5.877763e+00
17 (restart 0) KSP residual norm 5.474733e+00
18 (restart 0) KSP residual norm 4.630565e+00
19 (restart 0) KSP residual norm 3.634509e+00
20 (restart 0) KSP residual norm 3.514568e+00
21 (restart 0) KSP residual norm 2.798046e+00
22 (restart 0) KSP residual norm 2.708525e+00
23 (restart 0) KSP residual norm 2.604395e+00
24 (restart 0) KSP residual norm 2.347166e+00
25 (restart 0) KSP residual norm 2.300784e+00
26 (restart 0) KSP residual norm 2.074013e+00
27 (restart 0) KSP residual norm 1.846770e+00
28 (restart 0) KSP residual norm 1.791694e+00
29 (restart 0) KSP residual norm 1.545316e+00
30 (restart 0) KSP residual norm 1.525001e+00
31 (restart 0) KSP residual norm 1.368470e+00
32 (restart 0) KSP residual norm 1.261780e+00
33 (restart 0) KSP residual norm 1.230083e+00
34 (restart 0) KSP residual norm 1.159990e+00
35 (restart 0) KSP residual norm 1.086427e+00
36 (restart 0) KSP residual norm 1.053329e+00
37 (restart 0) KSP residual norm 9.459616e-01
38 (restart 0) KSP residual norm 9.315145e-01
39 (restart 0) KSP residual norm 8.197189e-01
40 (restart 0) KSP residual norm 6.798738e-01
41 (restart 0) KSP residual norm 6.559715e-01
42 (restart 0) KSP residual norm 6.112439e-01
43 (restart 0) KSP residual norm 5.553958e-01
44 (restart 0) KSP residual norm 5.191988e-01
45 (restart 0) KSP residual norm 4.636649e-01
46 (restart 0) KSP residual norm 4.131939e-01
47 (restart 0) KSP residual norm 3.974270e-01
48 (restart 0) KSP residual norm 3.580844e-01
49 (restart 0) KSP residual norm 3.408561e-01
50 (restart 0) KSP residual norm 3.153162e-01
51 (restart 0) KSP residual norm 2.890354e-01
52 (restart 0) KSP residual norm 2.699729e-01
53 (restart 0) KSP residual norm 2.431887e-01
54 (restart 0) KSP residual norm 2.210198e-01
55 (restart 0) KSP residual norm 1.941405e-01
56 (restart 0) KSP residual norm 1.855355e-01
57 (restart 0) KSP residual norm 1.647163e-01
58 (restart 0) KSP residual norm 1.501964e-01
59 (restart 0) KSP residual norm 1.419572e-01
60 (restart 0) KSP residual norm 1.303772e-01
61 (restart 0) KSP residual norm 1.198298e-01
62 (restart 0) KSP residual norm 1.127472e-01
63 (restart 0) KSP residual norm 1.038044e-01
64 (restart 0) KSP residual norm 9.477485e-02
65 (restart 0) KSP residual norm 8.890639e-02
66 (restart 0) KSP residual norm 7.894009e-02
67 (restart 0) KSP residual norm 7.398431e-02
68 (restart 0) KSP residual norm 6.820377e-02
69 (restart 0) KSP residual norm 6.358088e-02
70 (restart 0) KSP residual norm 5.513398e-02
71 (restart 0) KSP residual norm 4.923293e-02
72 (restart 0) KSP residual norm 4.551475e-02
73 (restart 0) KSP residual norm 4.115255e-02
74 (restart 0) KSP residual norm 3.814463e-02
75 (restart 0) KSP residual norm 3.434777e-02
76 (restart 0) KSP residual norm 3.209662e-02
77 (restart 0) KSP residual norm 2.879499e-02
78 (restart 0) KSP residual norm 2.661116e-02
79 (restart 0) KSP residual norm 2.445553e-02
80 (restart 0) KSP residual norm 2.162525e-02
81 (restart 0) KSP residual norm 2.001836e-02
82 (restart 0) KSP residual norm 1.777105e-02
83 (restart 0) KSP residual norm 1.630438e-02
84 (restart 0) KSP residual norm 1.469889e-02
85 (restart 0) KSP residual norm 1.339136e-02
86 (restart 0) KSP residual norm 1.183136e-02
87 (restart 0) KSP residual norm 1.016261e-02
88 (restart 0) KSP residual norm 8.907724e-03
89 (restart 0) KSP residual norm 7.949844e-03
90 (restart 0) KSP residual norm 7.165017e-03
91 (restart 0) KSP residual norm 6.508424e-03
92 (restart 0) KSP residual norm 5.620344e-03
93 (restart 0) KSP residual norm 4.941302e-03
94 (restart 0) KSP residual norm 4.388314e-03
95 (restart 0) KSP residual norm 3.838074e-03
96 (restart 0) KSP residual norm 3.485562e-03
97 (restart 0) KSP residual norm 3.090671e-03
98 (restart 0) KSP residual norm 2.720510e-03
99 (restart 0) KSP residual norm 2.402237e-03
100 (restart 0) KSP residual norm 2.078534e-03
101 (restart 0) KSP residual norm 1.787341e-03
102 (restart 0) KSP residual norm 1.558079e-03
103 (restart 0) KSP residual norm 1.381587e-03
104 (restart 0) KSP residual norm 1.180406e-03
105 (restart 0) KSP residual norm 9.804168e-04
106 (restart 0) KSP residual norm 7.973739e-04
107 (restart 0) KSP residual norm 6.484130e-04
108 (restart 0) KSP residual norm 5.210813e-04
109 (restart 0) KSP residual norm 4.234887e-04
110 (restart 0) KSP residual norm 3.562406e-04
111 (restart 0) KSP residual norm 3.046667e-04
112 (restart 0) KSP residual norm 2.665681e-04
113 (restart 0) KSP residual norm 2.284098e-04
114 (restart 0) KSP residual norm 1.935454e-04
115 (restart 0) KSP residual norm 1.638144e-04
116 (restart 0) KSP residual norm 1.450462e-04
117 (restart 0) KSP residual norm 1.255680e-04
118 (restart 0) KSP residual norm 1.051836e-04
119 (restart 0) KSP residual norm 8.399552e-05
120 (restart 0) KSP residual norm 6.732251e-05
121 (restart 0) KSP residual norm 5.597541e-05
122 (restart 0) KSP residual norm 4.656429e-05
123 (restart 0) KSP residual norm 3.974880e-05
124 (restart 0) KSP residual norm 3.263035e-05
125 (restart 0) KSP residual norm 2.709573e-05
126 (restart 0) KSP residual norm 2.188947e-05
127 (restart 0) KSP residual norm 1.737277e-05
128 (restart 0) KSP residual norm 1.424793e-05
129 (restart 0) KSP residual norm 1.212999e-05
130 (restart 0) KSP residual norm 1.027701e-05
131 (restart 0) KSP residual norm 8.532553e-06
132 (restart 0) KSP residual norm 6.983835e-06
133 (restart 0) KSP residual norm 5.776562e-06
134 (restart 0) KSP residual norm 4.880947e-06
135 (restart 0) KSP residual norm 4.040910e-06
136 (restart 0) KSP residual norm 3.331757e-06
137 (restart 0) KSP residual norm 2.773195e-06
138 (restart 0) KSP residual norm 2.288515e-06
139 (restart 0) KSP residual norm 1.906338e-06
140 (restart 0) KSP residual norm 1.594411e-06
141 (restart 0) KSP residual norm 1.339863e-06
142 (restart 0) KSP residual norm 1.133978e-06
143 (restart 0) KSP residual norm 9.348951e-07
144 (restart 0) KSP residual norm 7.776251e-07
145 (restart 0) KSP residual norm 6.358495e-07
146 (restart 0) KSP residual norm 5.235310e-07
147 (restart 0) KSP residual norm 4.397862e-07
148 (restart 0) KSP residual norm 3.741359e-07
149 (restart 0) KSP residual norm 3.087886e-07
GMRES solver converged in 149 iterations (avg. reduction factor: 8.832e-01)
Greedy iteration 1 (n = 4): ω* = 7.666e-02 GHz (1.928e+01), error = 1.807e-01
Field energy E (7.247e-01 J) + H (9.030e-02 J) = 8.150e-01 J
Residual norms for GMRES solve
0 (restart 0) KSP residual norm 4.201484e+01
1 (restart 0) KSP residual norm 3.699726e+01
2 (restart 0) KSP residual norm 2.479330e+01
3 (restart 0) KSP residual norm 1.978674e+01
4 (restart 0) KSP residual norm 1.756410e+01
5 (restart 0) KSP residual norm 1.146205e+01
6 (restart 0) KSP residual norm 1.114473e+01
7 (restart 0) KSP residual norm 1.024453e+01
8 (restart 0) KSP residual norm 1.006097e+01
9 (restart 0) KSP residual norm 7.483316e+00
10 (restart 0) KSP residual norm 7.370953e+00
11 (restart 0) KSP residual norm 6.756726e+00
12 (restart 0) KSP residual norm 6.433169e+00
13 (restart 0) KSP residual norm 6.371254e+00
14 (restart 0) KSP residual norm 5.770779e+00
15 (restart 0) KSP residual norm 5.752697e+00
16 (restart 0) KSP residual norm 5.007068e+00
17 (restart 0) KSP residual norm 4.636729e+00
18 (restart 0) KSP residual norm 4.289847e+00
19 (restart 0) KSP residual norm 4.088856e+00
20 (restart 0) KSP residual norm 3.928459e+00
21 (restart 0) KSP residual norm 3.632440e+00
22 (restart 0) KSP residual norm 3.608224e+00
23 (restart 0) KSP residual norm 3.429361e+00
24 (restart 0) KSP residual norm 3.365778e+00
25 (restart 0) KSP residual norm 3.306644e+00
26 (restart 0) KSP residual norm 3.122540e+00
27 (restart 0) KSP residual norm 3.064817e+00
28 (restart 0) KSP residual norm 2.919740e+00
29 (restart 0) KSP residual norm 2.724568e+00
30 (restart 0) KSP residual norm 2.659002e+00
31 (restart 0) KSP residual norm 2.379714e+00
32 (restart 0) KSP residual norm 2.316860e+00
33 (restart 0) KSP residual norm 2.145185e+00
34 (restart 0) KSP residual norm 2.034437e+00
35 (restart 0) KSP residual norm 1.960322e+00
36 (restart 0) KSP residual norm 1.766679e+00
37 (restart 0) KSP residual norm 1.720724e+00
38 (restart 0) KSP residual norm 1.526005e+00
39 (restart 0) KSP residual norm 1.341460e+00
40 (restart 0) KSP residual norm 1.321533e+00
41 (restart 0) KSP residual norm 1.027011e+00
42 (restart 0) KSP residual norm 9.981900e-01
43 (restart 0) KSP residual norm 8.371891e-01
44 (restart 0) KSP residual norm 7.741265e-01
45 (restart 0) KSP residual norm 7.259464e-01
46 (restart 0) KSP residual norm 6.237500e-01
47 (restart 0) KSP residual norm 6.017219e-01
48 (restart 0) KSP residual norm 5.079543e-01
49 (restart 0) KSP residual norm 4.861458e-01
50 (restart 0) KSP residual norm 4.337090e-01
51 (restart 0) KSP residual norm 3.896931e-01
52 (restart 0) KSP residual norm 3.533626e-01
53 (restart 0) KSP residual norm 3.193116e-01
54 (restart 0) KSP residual norm 2.925875e-01
55 (restart 0) KSP residual norm 2.692448e-01
56 (restart 0) KSP residual norm 2.486749e-01
57 (restart 0) KSP residual norm 2.284391e-01
58 (restart 0) KSP residual norm 2.114445e-01
59 (restart 0) KSP residual norm 1.903558e-01
60 (restart 0) KSP residual norm 1.791187e-01
61 (restart 0) KSP residual norm 1.568913e-01
62 (restart 0) KSP residual norm 1.488817e-01
63 (restart 0) KSP residual norm 1.308252e-01
64 (restart 0) KSP residual norm 1.237357e-01
65 (restart 0) KSP residual norm 1.098430e-01
66 (restart 0) KSP residual norm 1.011944e-01
67 (restart 0) KSP residual norm 9.240204e-02
68 (restart 0) KSP residual norm 7.853316e-02
69 (restart 0) KSP residual norm 7.343612e-02
70 (restart 0) KSP residual norm 5.878309e-02
71 (restart 0) KSP residual norm 5.418723e-02
72 (restart 0) KSP residual norm 4.712241e-02
73 (restart 0) KSP residual norm 4.292619e-02
74 (restart 0) KSP residual norm 3.713822e-02
75 (restart 0) KSP residual norm 3.221422e-02
76 (restart 0) KSP residual norm 2.643603e-02
77 (restart 0) KSP residual norm 2.344671e-02
78 (restart 0) KSP residual norm 2.164996e-02
79 (restart 0) KSP residual norm 1.970595e-02
80 (restart 0) KSP residual norm 1.718498e-02
81 (restart 0) KSP residual norm 1.461740e-02
82 (restart 0) KSP residual norm 1.296993e-02
83 (restart 0) KSP residual norm 1.121418e-02
84 (restart 0) KSP residual norm 9.927232e-03
85 (restart 0) KSP residual norm 9.008599e-03
86 (restart 0) KSP residual norm 7.513208e-03
87 (restart 0) KSP residual norm 6.588333e-03
88 (restart 0) KSP residual norm 5.677089e-03
89 (restart 0) KSP residual norm 5.061547e-03
90 (restart 0) KSP residual norm 4.623938e-03
91 (restart 0) KSP residual norm 4.037335e-03
92 (restart 0) KSP residual norm 3.489319e-03
93 (restart 0) KSP residual norm 2.876739e-03
94 (restart 0) KSP residual norm 2.537234e-03
95 (restart 0) KSP residual norm 2.287873e-03
96 (restart 0) KSP residual norm 2.072829e-03
97 (restart 0) KSP residual norm 1.753329e-03
98 (restart 0) KSP residual norm 1.540126e-03
99 (restart 0) KSP residual norm 1.330358e-03
100 (restart 0) KSP residual norm 1.206118e-03
101 (restart 0) KSP residual norm 1.093429e-03
102 (restart 0) KSP residual norm 9.551687e-04
103 (restart 0) KSP residual norm 8.326909e-04
104 (restart 0) KSP residual norm 7.239925e-04
105 (restart 0) KSP residual norm 6.478568e-04
106 (restart 0) KSP residual norm 5.835552e-04
107 (restart 0) KSP residual norm 5.188423e-04
108 (restart 0) KSP residual norm 4.379782e-04
109 (restart 0) KSP residual norm 3.629590e-04
110 (restart 0) KSP residual norm 3.116633e-04
111 (restart 0) KSP residual norm 2.759593e-04
112 (restart 0) KSP residual norm 2.430551e-04
113 (restart 0) KSP residual norm 2.005860e-04
114 (restart 0) KSP residual norm 1.599661e-04
115 (restart 0) KSP residual norm 1.257960e-04
116 (restart 0) KSP residual norm 1.015883e-04
117 (restart 0) KSP residual norm 8.714039e-05
118 (restart 0) KSP residual norm 7.794489e-05
119 (restart 0) KSP residual norm 6.627367e-05
120 (restart 0) KSP residual norm 5.348801e-05
121 (restart 0) KSP residual norm 4.438590e-05
122 (restart 0) KSP residual norm 3.652341e-05
123 (restart 0) KSP residual norm 3.132649e-05
124 (restart 0) KSP residual norm 2.551602e-05
125 (restart 0) KSP residual norm 2.170744e-05
126 (restart 0) KSP residual norm 1.708523e-05
127 (restart 0) KSP residual norm 1.403872e-05
128 (restart 0) KSP residual norm 1.104181e-05
129 (restart 0) KSP residual norm 9.319661e-06
130 (restart 0) KSP residual norm 7.628311e-06
131 (restart 0) KSP residual norm 6.452134e-06
132 (restart 0) KSP residual norm 5.026538e-06
133 (restart 0) KSP residual norm 4.120557e-06
134 (restart 0) KSP residual norm 3.259806e-06
135 (restart 0) KSP residual norm 2.662429e-06
136 (restart 0) KSP residual norm 2.101417e-06
137 (restart 0) KSP residual norm 1.750245e-06
138 (restart 0) KSP residual norm 1.414542e-06
139 (restart 0) KSP residual norm 1.144148e-06
140 (restart 0) KSP residual norm 8.743341e-07
141 (restart 0) KSP residual norm 7.071765e-07
142 (restart 0) KSP residual norm 5.551381e-07
143 (restart 0) KSP residual norm 4.571115e-07
144 (restart 0) KSP residual norm 3.601505e-07
GMRES solver converged in 144 iterations (avg. reduction factor: 8.790e-01)
Greedy iteration 2 (n = 6): ω* = 6.589e-02 GHz (1.657e+01), error = 3.881e-02
Field energy E (7.873e-01 J) + H (8.491e-02 J) = 8.722e-01 J
Residual norms for GMRES solve
0 (restart 0) KSP residual norm 2.844314e+01
1 (restart 0) KSP residual norm 2.644548e+01
2 (restart 0) KSP residual norm 2.275776e+01
3 (restart 0) KSP residual norm 1.769332e+01
4 (restart 0) KSP residual norm 1.765085e+01
5 (restart 0) KSP residual norm 1.594473e+01
6 (restart 0) KSP residual norm 1.479618e+01
7 (restart 0) KSP residual norm 1.457876e+01
8 (restart 0) KSP residual norm 1.095591e+01
9 (restart 0) KSP residual norm 9.658261e+00
10 (restart 0) KSP residual norm 7.274301e+00
11 (restart 0) KSP residual norm 7.195220e+00
12 (restart 0) KSP residual norm 5.954279e+00
13 (restart 0) KSP residual norm 5.816909e+00
14 (restart 0) KSP residual norm 4.951125e+00
15 (restart 0) KSP residual norm 4.816588e+00
16 (restart 0) KSP residual norm 4.464790e+00
17 (restart 0) KSP residual norm 4.182610e+00
18 (restart 0) KSP residual norm 3.843518e+00
19 (restart 0) KSP residual norm 3.677767e+00
20 (restart 0) KSP residual norm 3.288194e+00
21 (restart 0) KSP residual norm 3.217689e+00
22 (restart 0) KSP residual norm 2.837661e+00
23 (restart 0) KSP residual norm 2.723380e+00
24 (restart 0) KSP residual norm 2.522806e+00
25 (restart 0) KSP residual norm 2.370371e+00
26 (restart 0) KSP residual norm 2.214101e+00
27 (restart 0) KSP residual norm 2.107167e+00
28 (restart 0) KSP residual norm 1.912278e+00
29 (restart 0) KSP residual norm 1.819147e+00
30 (restart 0) KSP residual norm 1.569321e+00
31 (restart 0) KSP residual norm 1.504773e+00
32 (restart 0) KSP residual norm 1.344828e+00
33 (restart 0) KSP residual norm 1.291095e+00
34 (restart 0) KSP residual norm 1.213578e+00
35 (restart 0) KSP residual norm 1.109702e+00
36 (restart 0) KSP residual norm 1.035425e+00
37 (restart 0) KSP residual norm 9.001570e-01
38 (restart 0) KSP residual norm 8.562292e-01
39 (restart 0) KSP residual norm 7.708716e-01
40 (restart 0) KSP residual norm 7.215291e-01
41 (restart 0) KSP residual norm 6.529219e-01
42 (restart 0) KSP residual norm 6.174605e-01
43 (restart 0) KSP residual norm 5.573557e-01
44 (restart 0) KSP residual norm 5.290993e-01
45 (restart 0) KSP residual norm 4.223429e-01
46 (restart 0) KSP residual norm 4.104930e-01
47 (restart 0) KSP residual norm 3.345857e-01
48 (restart 0) KSP residual norm 3.248134e-01
49 (restart 0) KSP residual norm 2.842468e-01
50 (restart 0) KSP residual norm 2.779873e-01
51 (restart 0) KSP residual norm 2.314581e-01
52 (restart 0) KSP residual norm 2.241979e-01
53 (restart 0) KSP residual norm 1.941883e-01
54 (restart 0) KSP residual norm 1.873997e-01
55 (restart 0) KSP residual norm 1.620324e-01
56 (restart 0) KSP residual norm 1.479451e-01
57 (restart 0) KSP residual norm 1.393785e-01
58 (restart 0) KSP residual norm 1.198478e-01
59 (restart 0) KSP residual norm 1.141420e-01
60 (restart 0) KSP residual norm 9.751654e-02
61 (restart 0) KSP residual norm 9.458212e-02
62 (restart 0) KSP residual norm 7.867308e-02
63 (restart 0) KSP residual norm 7.226444e-02
64 (restart 0) KSP residual norm 6.587274e-02
65 (restart 0) KSP residual norm 5.982050e-02
66 (restart 0) KSP residual norm 5.655181e-02
67 (restart 0) KSP residual norm 5.175948e-02
68 (restart 0) KSP residual norm 4.502918e-02
69 (restart 0) KSP residual norm 4.254858e-02
70 (restart 0) KSP residual norm 3.698099e-02
71 (restart 0) KSP residual norm 3.360218e-02
72 (restart 0) KSP residual norm 3.114946e-02
73 (restart 0) KSP residual norm 2.696771e-02
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83 (restart 0) KSP residual norm 7.527019e-03
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129 (restart 0) KSP residual norm 7.765352e-06
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135 (restart 0) KSP residual norm 2.553050e-06
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137 (restart 0) KSP residual norm 1.720958e-06
138 (restart 0) KSP residual norm 1.376295e-06
139 (restart 0) KSP residual norm 1.114133e-06
140 (restart 0) KSP residual norm 9.030977e-07
141 (restart 0) KSP residual norm 7.458604e-07
142 (restart 0) KSP residual norm 6.015027e-07
143 (restart 0) KSP residual norm 4.891975e-07
144 (restart 0) KSP residual norm 3.990345e-07
145 (restart 0) KSP residual norm 3.217504e-07
146 (restart 0) KSP residual norm 2.588682e-07
GMRES solver converged in 146 iterations (avg. reduction factor: 8.809e-01)
Greedy iteration 3 (n = 8): ω* = 8.747e-02 GHz (2.200e+01), error = 2.281e-03
Field energy E (6.715e-01 J) + H (9.586e-02 J) = 7.673e-01 J
Residual norms for GMRES solve
0 (restart 0) KSP residual norm 2.042889e+01
1 (restart 0) KSP residual norm 2.027437e+01
2 (restart 0) KSP residual norm 2.023083e+01
3 (restart 0) KSP residual norm 1.547535e+01
4 (restart 0) KSP residual norm 1.502530e+01
5 (restart 0) KSP residual norm 1.318760e+01
6 (restart 0) KSP residual norm 1.133267e+01
7 (restart 0) KSP residual norm 8.630884e+00
8 (restart 0) KSP residual norm 7.896093e+00
9 (restart 0) KSP residual norm 6.428616e+00
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11 (restart 0) KSP residual norm 5.268262e+00
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13 (restart 0) KSP residual norm 4.728123e+00
14 (restart 0) KSP residual norm 4.552161e+00
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17 (restart 0) KSP residual norm 3.785865e+00
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30 (restart 0) KSP residual norm 9.869732e-01
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136 (restart 0) KSP residual norm 2.570930e-07
137 (restart 0) KSP residual norm 2.060828e-07
138 (restart 0) KSP residual norm 1.630016e-07
GMRES solver converged in 138 iterations (avg. reduction factor: 8.736e-01)
Greedy iteration 4 (n = 10): ω* = 5.987e-02 GHz (1.506e+01), error = 2.983e-04, memory = 1/2
Field energy E (8.263e-01 J) + H (8.124e-02 J) = 9.076e-01 J
Residual norms for GMRES solve
0 (restart 0) KSP residual norm 4.019291e+02
1 (restart 0) KSP residual norm 3.268955e+01
2 (restart 0) KSP residual norm 2.986973e+01
3 (restart 0) KSP residual norm 1.696305e+01
4 (restart 0) KSP residual norm 1.692442e+01
5 (restart 0) KSP residual norm 1.362762e+01
6 (restart 0) KSP residual norm 1.315620e+01
7 (restart 0) KSP residual norm 1.245182e+01
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10 (restart 0) KSP residual norm 9.496582e+00
11 (restart 0) KSP residual norm 9.310563e+00
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40 (restart 0) KSP residual norm 3.829883e-01
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67 (restart 0) KSP residual norm 1.157376e-02
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70 (restart 0) KSP residual norm 8.468033e-03
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103 (restart 0) KSP residual norm 8.723157e-05
104 (restart 0) KSP residual norm 7.608098e-05
105 (restart 0) KSP residual norm 6.509107e-05
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115 (restart 0) KSP residual norm 1.235002e-05
116 (restart 0) KSP residual norm 1.049758e-05
117 (restart 0) KSP residual norm 8.930803e-06
118 (restart 0) KSP residual norm 7.808016e-06
119 (restart 0) KSP residual norm 6.769262e-06
120 (restart 0) KSP residual norm 5.799267e-06
121 (restart 0) KSP residual norm 5.047058e-06
122 (restart 0) KSP residual norm 4.367123e-06
123 (restart 0) KSP residual norm 3.839456e-06
GMRES solver converged in 123 iterations (avg. reduction factor: 8.606e-01)
Greedy iteration 5 (n = 12): ω* = 9.128e-02 GHz (2.296e+01), error = 9.899e-05, memory = 2/2
Field energy E (6.537e-01 J) + H (9.701e-02 J) = 7.507e-01 J
Adaptive sampling converged with 7 frequency samples:
n = 14, error = 9.899e-05, tol = 1.000e-03, memory = 2/2
Sampled frequencies (GHz): 5.621e-02, 9.369e-02, 7.666e-02, 6.589e-02,
8.747e-02, 5.987e-02, 9.128e-02
Sample errors: inf, inf, 1.807e-01, 3.881e-02, 2.281e-03,
2.983e-04, 9.899e-05
Total offline phase elapsed time: 1.28e+02 s
Beginning fast frequency sweep online phase
It 1/21: ω/2π = 5.621e-02 GHz (total elapsed time = 1.28e+02 s)
Sol. ||E|| = 7.552320e+00
Field energy E (8.510e-01 J) + H (7.806e-02 J) = 9.290e-01 J
S[1][1] = +7.634e-01-2.730e-01i, |S[1][1]| = -1.823e+00, arg(S[1][1]) = -1.968e+01
Wrote fields to disk (Paraview) at step 1
It 2/21: ω/2π = 5.808e-02 GHz (total elapsed time = 1.29e+02 s)
Sol. ||E|| = 7.487982e+00
Field energy E (8.382e-01 J) + H (7.977e-02 J) = 9.180e-01 J
S[1][1] = +7.569e-01-2.768e-01i, |S[1][1]| = -1.874e+00, arg(S[1][1]) = -2.009e+01
It 3/21: ω/2π = 5.996e-02 GHz (total elapsed time = 1.30e+02 s)
Sol. ||E|| = 7.424728e+00
Field energy E (8.257e-01 J) + H (8.131e-02 J) = 9.070e-01 J
S[1][1] = +7.504e-01-2.804e-01i, |S[1][1]| = -1.926e+00, arg(S[1][1]) = -2.049e+01
It 4/21: ω/2π = 6.183e-02 GHz (total elapsed time = 1.31e+02 s)
Sol. ||E|| = 7.362445e+00
Field energy E (8.134e-01 J) + H (8.264e-02 J) = 8.960e-01 J
S[1][1] = +7.440e-01-2.839e-01i, |S[1][1]| = -1.979e+00, arg(S[1][1]) = -2.089e+01
It 5/21: ω/2π = 6.371e-02 GHz (total elapsed time = 1.32e+02 s)
Sol. ||E|| = 7.301097e+00
Field energy E (8.013e-01 J) + H (8.378e-02 J) = 8.850e-01 J
S[1][1] = +7.376e-01-2.872e-01i, |S[1][1]| = -2.031e+00, arg(S[1][1]) = -2.127e+01
It 6/21: ω/2π = 6.558e-02 GHz (total elapsed time = 1.34e+02 s)
Sol. ||E|| = 7.240704e+00
Field energy E (7.893e-01 J) + H (8.476e-02 J) = 8.740e-01 J
S[1][1] = +7.312e-01-2.903e-01i, |S[1][1]| = -2.083e+00, arg(S[1][1]) = -2.165e+01
Wrote fields to disk (Paraview) at step 6
It 7/21: ω/2π = 6.745e-02 GHz (total elapsed time = 1.36e+02 s)
Sol. ||E|| = 7.181323e+00
Field energy E (7.775e-01 J) + H (8.565e-02 J) = 8.632e-01 J
S[1][1] = +7.250e-01-2.932e-01i, |S[1][1]| = -2.135e+00, arg(S[1][1]) = -2.202e+01
It 8/21: ω/2π = 6.933e-02 GHz (total elapsed time = 1.37e+02 s)
Sol. ||E|| = 7.123018e+00
Field energy E (7.661e-01 J) + H (8.651e-02 J) = 8.526e-01 J
S[1][1] = +7.188e-01-2.960e-01i, |S[1][1]| = -2.187e+00, arg(S[1][1]) = -2.238e+01
It 9/21: ω/2π = 7.120e-02 GHz (total elapsed time = 1.39e+02 s)
Sol. ||E|| = 7.065844e+00
Field energy E (7.549e-01 J) + H (8.738e-02 J) = 8.423e-01 J
S[1][1] = +7.127e-01-2.986e-01i, |S[1][1]| = -2.239e+00, arg(S[1][1]) = -2.273e+01
It 10/21: ω/2π = 7.307e-02 GHz (total elapsed time = 1.40e+02 s)
Sol. ||E|| = 7.009826e+00
Field energy E (7.442e-01 J) + H (8.832e-02 J) = 8.325e-01 J
S[1][1] = +7.067e-01-3.011e-01i, |S[1][1]| = -2.291e+00, arg(S[1][1]) = -2.308e+01
It 11/21: ω/2π = 7.495e-02 GHz (total elapsed time = 1.42e+02 s)
Sol. ||E|| = 6.954951e+00
Field energy E (7.338e-01 J) + H (8.932e-02 J) = 8.231e-01 J
S[1][1] = +7.008e-01-3.035e-01i, |S[1][1]| = -2.342e+00, arg(S[1][1]) = -2.342e+01
Wrote fields to disk (Paraview) at step 11
It 12/21: ω/2π = 7.682e-02 GHz (total elapsed time = 1.44e+02 s)
Sol. ||E|| = 6.901167e+00
Field energy E (7.238e-01 J) + H (9.039e-02 J) = 8.142e-01 J
S[1][1] = +6.949e-01-3.057e-01i, |S[1][1]| = -2.393e+00, arg(S[1][1]) = -2.375e+01
It 13/21: ω/2π = 7.870e-02 GHz (total elapsed time = 1.46e+02 s)
Sol. ||E|| = 6.848395e+00
Field energy E (7.141e-01 J) + H (9.149e-02 J) = 8.056e-01 J
S[1][1] = +6.891e-01-3.079e-01i, |S[1][1]| = -2.444e+00, arg(S[1][1]) = -2.407e+01
It 14/21: ω/2π = 8.057e-02 GHz (total elapsed time = 1.48e+02 s)
Sol. ||E|| = 6.796535e+00
Field energy E (7.047e-01 J) + H (9.259e-02 J) = 7.973e-01 J
S[1][1] = +6.834e-01-3.099e-01i, |S[1][1]| = -2.494e+00, arg(S[1][1]) = -2.439e+01
It 15/21: ω/2π = 8.244e-02 GHz (total elapsed time = 1.50e+02 s)
Sol. ||E|| = 6.745491e+00
Field energy E (6.955e-01 J) + H (9.362e-02 J) = 7.891e-01 J
S[1][1] = +6.778e-01-3.118e-01i, |S[1][1]| = -2.545e+00, arg(S[1][1]) = -2.470e+01
It 16/21: ω/2π = 8.432e-02 GHz (total elapsed time = 1.53e+02 s)
Sol. ||E|| = 6.695180e+00
Field energy E (6.864e-01 J) + H (9.456e-02 J) = 7.810e-01 J
S[1][1] = +6.722e-01-3.136e-01i, |S[1][1]| = -2.595e+00, arg(S[1][1]) = -2.501e+01
Wrote fields to disk (Paraview) at step 16
It 17/21: ω/2π = 8.619e-02 GHz (total elapsed time = 1.55e+02 s)
Sol. ||E|| = 6.645555e+00
Field energy E (6.775e-01 J) + H (9.538e-02 J) = 7.729e-01 J
S[1][1] = +6.667e-01-3.152e-01i, |S[1][1]| = -2.645e+00, arg(S[1][1]) = -2.531e+01
It 18/21: ω/2π = 8.806e-02 GHz (total elapsed time = 1.58e+02 s)
Sol. ||E|| = 6.596610e+00
Field energy E (6.686e-01 J) + H (9.607e-02 J) = 7.647e-01 J
S[1][1] = +6.613e-01-3.168e-01i, |S[1][1]| = -2.695e+00, arg(S[1][1]) = -2.560e+01
It 19/21: ω/2π = 8.994e-02 GHz (total elapsed time = 1.60e+02 s)
Sol. ||E|| = 6.548375e+00
Field energy E (6.599e-01 J) + H (9.665e-02 J) = 7.565e-01 J
S[1][1] = +6.560e-01-3.183e-01i, |S[1][1]| = -2.744e+00, arg(S[1][1]) = -2.588e+01
It 20/21: ω/2π = 9.181e-02 GHz (total elapsed time = 1.63e+02 s)
Sol. ||E|| = 6.500909e+00
Field energy E (6.513e-01 J) + H (9.715e-02 J) = 7.484e-01 J
S[1][1] = +6.507e-01-3.197e-01i, |S[1][1]| = -2.793e+00, arg(S[1][1]) = -2.616e+01
It 21/21: ω/2π = 9.369e-02 GHz (total elapsed time = 1.66e+02 s)
Sol. ||E|| = 6.454280e+00
Field energy E (6.429e-01 J) + H (9.762e-02 J) = 7.405e-01 J
S[1][1] = +6.456e-01-3.210e-01i, |S[1][1]| = -2.842e+00, arg(S[1][1]) = -2.644e+01
Wrote fields to disk (Paraview) at step 21
Completed 0 iterations of adaptive mesh refinement (AMR):
Indicator norm = 3.831e-01, global unknowns = 59472
Max. iterations = 0, tol. = 1.000e-02
Elapsed Time Report (s) Min. Max. Avg.
==============================================================
Initialization 0.067 0.070 0.069
Mesh Preprocessing 0.159 0.162 0.159
Operator Construction 0.608 17.963 16.872
Linear Solve 17.294 17.667 17.404
Setup 6.254 6.260 6.258
Preconditioner 87.633 90.224 89.156
Coarse Solve 11.349 13.613 12.356
PROM Construction 0.165 0.171 0.166
PROM Solve 0.006 0.008 0.006
Estimation 0.038 0.049 0.041
Construction 0.659 0.661 0.660
Solve 2.575 2.580 2.577
Postprocessing 0.294 23.158 1.727
Far Fields 16.642 16.665 16.654
Paraview 1.289 6.790 6.444
Disk IO 0.081 0.081 0.081
--------------------------------------------------------------
Total 170.707 170.707 170.707
# S parameters. Return the frequency where the minimum is reached.
from pathlib import Path
from palacetoolkit.postpro import s_params
notebook_dir = Path().resolve()
postpro_dir = notebook_dir / "postpro" / "dipole_antenna"
f = s_params(str(postpro_dir / "port-S.csv"))
