Patch Antenna#
We now apply a refined mesh for the patch antenna. Because the electromagnetic fields change rapidly near the metallic patch and the substrate edges, we increase the mesh density in these areas to ensure high simulation accuracy for resonance and radiation patterns.
import gmsh
import math
from palacetoolkit.plot_farfield import load_data, polar_plots, three_d_plot
from palacetoolkit.postpro import s_params
from palacetoolkit.simulation import generate_palace_config_from_entities
from palacetoolkit.viz import view_mesh
from palacetoolkit.mesh import (
Entity,
run_meshing_pipeline,
generate_3d_mesh,
refine_near_surfaces
)
Parameters:#
l : Patch length along x-axis, specified as a scalar in meters.
w : Patch width along y-axis, specified as a scalar in meters.
h : Patch height along z-axis, specified as a scalar in meters.
l1 : Ground plane length along x-axis, specified as a scalar in meters
w1 : Ground plane width along y-axis, specified as a scalar in meters
l2 : Notch length along x-axis, specified as a scalar in meters.
w2 : Notch width along x-axis, specified as a scalar in meters.
w3 : Strip line width along y-axis, specified as a scalar in meters.
airsphere_radius : Air sphere radius, specified as a scalar in meters.
freq : Simulation frequency in GHz, specified as a scalar.
filename : Output mesh filename, specified as a string.
eps_r: relative permittivity of the substrate
loss_tan: loss tangent of the substrate
port_impedance: characteristic impedance of the lumped port (Ohms)
# Patch
l: float = 0.030
w: float = 0.029
# Ground plane
l1: float = 0.06
w1: float = 0.06
# Notch
l2: float = 0.008
w2: float = 0.003
# Feed line
w3: float = 0.002
# Substrate
h: float = 0.0013
freq: float = 3.3
eps_r: float = 2.2
loss_tan: float = 0.0009
mu_r = 1.0
port_impedance: float = 50.0
wavelength = 3e8 / (freq * 1e9)
# Air sphere
airsphere_radius: float = wavelength
# Filename where the mesh is loadeds
filename = "patch_antenna.msh"
Initialize the model#
gmsh.initialize()
gmsh.model.add("patch_antenna")
kernel = gmsh.model.occ
Geometry Construction#
In this step, we build the physical structure of the patch antenna. We define the substrate, the metallic ground plane, and the antenna patch itself.
Patch Design: We combine the main patch and the feed line, including an inset to help with impedance matching. Excitation: A lumped port is created and positioned to feed the antenna. Domain Setup: We enclose the entire structure in an “air sphere,” which defines the simulation region (the radiation space). Finalizing: We use boolean operations (fragmenting) to ensure all components are properly connected and recognized as a single cohesive model by the solver.
substrate = kernel.addBox(-l1/2, -w1/2, 0, l1, w1, h)
# Ground plane
ground_plane = kernel.addRectangle(-l1/2, -w1/2, 0, l1, w1)
# Patch definition
main_patch = kernel.addRectangle(-l/2, -w/2, h, l, w)
inset = kernel.addRectangle(-l/2, -w2/2, h, l2, w2)
patch_dimtags, _ = kernel.cut(
[(2, main_patch)],
[(2, inset)],
removeObject=True, removeTool=True
)
kernel.synchronize()
feed_length = (l1 - l)/2 + l2
feed_line = kernel.addRectangle(-l1/2, -w3/2, h, feed_length, w3)
# Our patch
top_conductor, _ = kernel.fuse(
patch_dimtags, [(2, feed_line)],
removeObject=True, removeTool=True
)
kernel.synchronize()
# Gap bewteen the gropund plane and the bottom of the lumped port.
lumped_port = kernel.addRectangle(-l1/2, -w3/2, 0, h, w3)
kernel.rotate([(2, lumped_port)], -l1/2, 0, 0, 0, 1, 0, -math.pi/2)
kernel.synchronize()
def create_air_sphere(airsphere_radius: float) -> int:
return kernel.addSphere(0.0, 0.0, 0.0, airsphere_radius)
air_sphere = create_air_sphere(airsphere_radius)
kernel.synchronize()
Info : Cannot bind existing OpenCASCADE surface 8 to second tag 9
Info : Could not preserve tag of 2D object 9 (->8)
Entities definition and mesh refinement.#
# Define the entities which later will become the physical groups.
entities = [
Entity("air_sphere", dim = 3, mesh_order = 2, btype = "dielectric", tags = [air_sphere], loss_tan = 0.0, eps_r = 1.0, mu_r = 1.0),
Entity("substrate", dim = 3, mesh_order = 1, btype = "dielectric", tags = [substrate], loss_tan = loss_tan, eps_r = eps_r, mu_r = mu_r),
Entity("top_conductor", dim = 2, mesh_order= 1, btype = "pec", tags = [top_conductor[0][1]]),
Entity("ground_plane", dim = 2, mesh_order = 1, btype = "pec", tags = [ground_plane]),
Entity("lumped_port", dim = 2, mesh_order = 0, btype = "lumped_port", tags = [lumped_port], R = port_impedance, direction = '+Z', excitation = True)
]
# Boolean operations to guarantee a nice mesh, algo it returns the
# physical group map.
pg_map = run_meshing_pipeline(entities)
# Refine near the top conductor and locally the lumped port
refine_near_surfaces(entities[2].dimtags + entities[-1].dimtags,
wavelength,
ppw_near=400,
ppw_far=5,
transition_distance=wavelength/4,
set_as_background=True)
# # Mesh sizes
# mesh_sizes = {
# "substrate": wavelength / 12,
# "air_sphere": wavelength / 4,
# "lumped_port": wavelength / 150,
# "ground_plane" : wavelength / 10,
# "top_conductor": wavelength / 50
# }
generate_3d_mesh(entities, output_file=filename, optimize=True)
gmsh.option.setNumber("Mesh.MshFileVersion", 2.2)
gmsh.write(filename)
gmsh.finalize()
Physical group 'air_sphere' (dim=3): pg=1, tags=[2]
Physical group 'substrate' (dim=3): pg=2, tags=[1]
Physical group 'top_conductor' (dim=2): pg=3, tags=[8]
Physical group 'ground_plane' (dim=2): pg=4, tags=[7]
Physical group 'lumped_port' (dim=2): pg=5, tags=[9]
Physical group 'air_sphere__None' (dim=2): pg=6, tags=[16]
Physical group 'air_sphere__substrate' (dim=2): pg=7, tags=[10, 11, 13, 15, 14, 12]
ppw_near=400 ppw_far=5
SizeMax=0.0182 transition=0.0227
global: 15 curves, SizeMin=0.0002
Info : Meshing 1D...
Info : [ 0%] Meshing curve 45 (Line)
Info : [ 10%] Meshing curve 46 (Line)
Info : [ 10%] Meshing curve 47 (Line)
Info : [ 10%] Meshing curve 48 (Line)
Info : [ 20%] Meshing curve 49 (Line)
Info : [ 20%] Meshing curve 50 (Line)
Info : [ 20%] Meshing curve 51 (Line)
Info : [ 30%] Meshing curve 52 (Line)
Info : [ 30%] Meshing curve 53 (Line)
Info : [ 30%] Meshing curve 54 (Line)
Info : [ 40%] Meshing curve 55 (Line)
Info : [ 40%] Meshing curve 56 (Line)
Info : [ 40%] Meshing curve 57 (Line)
Info : [ 50%] Meshing curve 58 (Line)
Info : [ 50%] Meshing curve 59 (Line)
Info : [ 50%] Meshing curve 60 (Line)
Info : [ 60%] Meshing curve 61 (Line)
Info : [ 60%] Meshing curve 62 (Line)
Info : [ 60%] Meshing curve 63 (Line)
Info : [ 60%] Meshing curve 64 (Line)
Info : [ 70%] Meshing curve 65 (Line)
Info : [ 70%] Meshing curve 66 (Line)
Info : [ 70%] Meshing curve 67 (Line)
Info : [ 80%] Meshing curve 68 (Line)
Info : [ 80%] Meshing curve 69 (Line)
Info : [ 80%] Meshing curve 70 (Line)
Info : [ 90%] Meshing curve 71 (Line)
Info : [ 90%] Meshing curve 72 (Line)
Info : [100%] Meshing curve 74 (Circle)
Info : [100%] Meshing curve 76 (Line)
Info : Done meshing 1D (Wall 0.236431s, CPU 0.227489s)
Info : Meshing 2D...
Info : [ 0%] Meshing surface 7 (Plane, MeshAdapt)
Info : [ 20%] Meshing surface 8 (Plane, MeshAdapt)
Info : [ 30%] Meshing surface 9 (Plane, MeshAdapt)
Info : [ 40%] Meshing surface 10 (Plane, MeshAdapt)
Info : [ 50%] Meshing surface 11 (Plane, MeshAdapt)
Info : [ 60%] Meshing surface 12 (Plane, MeshAdapt)
Info : [ 70%] Meshing surface 13 (Plane, MeshAdapt)
Info : [ 80%] Meshing surface 14 (Plane, MeshAdapt)
Info : [ 90%] Meshing surface 15 (Plane, MeshAdapt)
Info : [100%] Meshing surface 16 (Sphere, MeshAdapt)
Info : Done meshing 2D (Wall 0.373643s, CPU 0.371467s)
Info : Meshing 3D...
Info : 3D Meshing 2 volumes with 1 connected component
Info : Tetrahedrizing 3397 nodes...
Info : Done tetrahedrizing 3405 nodes (Wall 0.0230094s, CPU 0.023024s)
Info : Reconstructing mesh...
Info : - Creating surface mesh
Info : - Identifying boundary edges
Info : - Recovering boundary
Info : Done reconstructing mesh (Wall 0.0450368s, CPU 0.044711s)
Info : Found volume 2
Info : Found volume 1
Info : It. 0 - 0 nodes created - worst tet radius 11.0285 (nodes removed 0 0)
Info : It. 500 - 500 nodes created - worst tet radius 1.43714 (nodes removed 0 0)
Info : It. 1000 - 1000 nodes created - worst tet radius 1.17669 (nodes removed 0 0)
Info : It. 1500 - 1500 nodes created - worst tet radius 1.03815 (nodes removed 0 0)
Info : 3D refinement terminated (5056 nodes total):
Info : - 1 Delaunay cavities modified for star shapeness
Info : - 0 nodes could not be inserted
Info : - 28108 tetrahedra created in 0.102852 sec. (273286 tets/s)
Info : 0 node relocations
Info : Done meshing 3D (Wall 0.196644s, CPU 0.196658s)
Info : Optimizing mesh...
Info : Optimizing volume 1
Info : Optimization starts (volume = 4.68e-06) with worst = 0.00812265 / average = 0.606544:
Info : 0.00 < quality < 0.10 : 32 elements
Info : 0.10 < quality < 0.20 : 103 elements
Info : 0.20 < quality < 0.30 : 252 elements
Info : 0.30 < quality < 0.40 : 666 elements
Info : 0.40 < quality < 0.50 : 1737 elements
Info : 0.50 < quality < 0.60 : 2185 elements
Info : 0.60 < quality < 0.70 : 2006 elements
Info : 0.70 < quality < 0.80 : 1616 elements
Info : 0.80 < quality < 0.90 : 1061 elements
Info : 0.90 < quality < 1.00 : 416 elements
Info : 289 edge swaps, 11 node relocations (volume = 4.68e-06): worst = 0.146028 / average = 0.618471 (Wall 0.0025048s, CPU 0.002533s)
Info : 304 edge swaps, 15 node relocations (volume = 4.68e-06): worst = 0.158684 / average = 0.618763 (Wall 0.00341546s, CPU 0.003466s)
Info : 308 edge swaps, 17 node relocations (volume = 4.68e-06): worst = 0.158684 / average = 0.61881 (Wall 0.00427831s, CPU 0.00435s)
Info : No ill-shaped tets in the mesh :-)
Info : 0.00 < quality < 0.10 : 0 elements
Info : 0.10 < quality < 0.20 : 6 elements
Info : 0.20 < quality < 0.30 : 84 elements
Info : 0.30 < quality < 0.40 : 712 elements
Info : 0.40 < quality < 0.50 : 1706 elements
Info : 0.50 < quality < 0.60 : 2169 elements
Info : 0.60 < quality < 0.70 : 2023 elements
Info : 0.70 < quality < 0.80 : 1631 elements
Info : 0.80 < quality < 0.90 : 1092 elements
Info : 0.90 < quality < 1.00 : 409 elements
Info : Optimizing volume 2
Info : Optimization starts (volume = 0.00309809) with worst = 0.0111154 / average = 0.620966:
Info : 0.00 < quality < 0.10 : 76 elements
Info : 0.10 < quality < 0.20 : 294 elements
Info : 0.20 < quality < 0.30 : 433 elements
Info : 0.30 < quality < 0.40 : 1064 elements
Info : 0.40 < quality < 0.50 : 2553 elements
Info : 0.50 < quality < 0.60 : 3613 elements
Info : 0.60 < quality < 0.70 : 3699 elements
Info : 0.70 < quality < 0.80 : 3145 elements
Info : 0.80 < quality < 0.90 : 2391 elements
Info : 0.90 < quality < 1.00 : 766 elements
Info : 673 edge swaps, 61 node relocations (volume = 0.00309809): worst = 0.0962665 / average = 0.637204 (Wall 0.00600244s, CPU 0.006037s)
Info : 708 edge swaps, 74 node relocations (volume = 0.00309809): worst = 0.0962665 / average = 0.637422 (Wall 0.00803917s, CPU 0.00811s)
Info : No ill-shaped tets in the mesh :-)
Info : 0.00 < quality < 0.10 : 1 elements
Info : 0.10 < quality < 0.20 : 33 elements
Info : 0.20 < quality < 0.30 : 47 elements
Info : 0.30 < quality < 0.40 : 1146 elements
Info : 0.40 < quality < 0.50 : 2503 elements
Info : 0.50 < quality < 0.60 : 3605 elements
Info : 0.60 < quality < 0.70 : 3723 elements
Info : 0.70 < quality < 0.80 : 3189 elements
Info : 0.80 < quality < 0.90 : 2405 elements
Info : 0.90 < quality < 1.00 : 769 elements
Info : Done optimizing mesh (Wall 0.0239096s, CPU 0.024129s)
Info : 5056 nodes 35023 elements
Info : Optimizing mesh (Netgen)...
Info : Optimizing volume 1
Info : CalcLocalH: 3265 Points 9839 Elements 5952 Surface Elements
Info : Remove Illegal Elements
Info : 188 illegal tets
Info : SplitImprove
Info : badmax = 193.075
Info : 25 splits performed
Info : SwapImprove
Info : 23 swaps performed
Info : SwapImprove2
Info : 0 swaps performed
Info : 150 illegal tets
Info : SplitImprove
Info : badmax = 193.075
Info : 29 splits performed
Info : SwapImprove
Info : 9 swaps performed
Info : SwapImprove2
Info : 3 swaps performed
Info : 86 illegal tets
Info : SplitImprove
Info : badmax = 3349.48
Info : 24 splits performed
Info : SwapImprove
Info : 5 swaps performed
Info : SwapImprove2
Info : 2 swaps performed
Info : 26 illegal tets
Info : SplitImprove
Info : badmax = 1865.02
Info : 9 splits performed
Info : SwapImprove
Info : 2 swaps performed
Info : SwapImprove2
Info : 1 swaps performed
Info : 8 illegal tets
Info : SplitImprove
Info : badmax = 411.944
Info : 3 splits performed
Info : SwapImprove
Info : 0 swaps performed
Info : SwapImprove2
Info : 0 swaps performed
Info : 0 illegal tets
Info : Volume Optimization
Info : CombineImprove
Info : 27 elements combined
Info : ImproveMesh
Info : Total badness = 21659.3
Info : Total badness = 19580.3
Info : SplitImprove
Info : badmax = 135.164
Info : 1 splits performed
Info : ImproveMesh
Info : Total badness = 19588.1
Info : Total badness = 19505.8
Info : SwapImprove
Info : 477 swaps performed
Info : SwapImprove2
Info : 0 swaps performed
Info : ImproveMesh
Info : Total badness = 18595.8
Info : Total badness = 18407.6
Info : CombineImprove
Info : 1 elements combined
Info : ImproveMesh
Info : Total badness = 18398
Info : Total badness = 18389.7
Info : SplitImprove
Info : badmax = 85.9383
Info : 2 splits performed
Info : ImproveMesh
Info : Total badness = 18404.5
Info : Total badness = 18403.9
Info : SwapImprove
Info : 124 swaps performed
Info : SwapImprove2
Info : 0 swaps performed
Info : ImproveMesh
Info : Total badness = 18282.4
Info : Total badness = 18197.2
Info : CombineImprove
Info : 2 elements combined
Info : ImproveMesh
Info : Total badness = 18166.1
Info : Total badness = 18161
Info : SplitImprove
Info : badmax = 85.934
Info : 0 splits performed
Info : ImproveMesh
Info : Total badness = 18161
Info : Total badness = 18160.6
Info : SwapImprove
Info : 50 swaps performed
Info : SwapImprove2
Info : 0 swaps performed
Info : ImproveMesh
Info : Total badness = 18098.4
Info : Total badness = 18061.9
Info : Optimizing volume 2
Info : CalcLocalH: 4769 Points 17490 Elements 6786 Surface Elements
Info : Remove Illegal Elements
Info : 0 illegal tets
Info : Volume Optimization
Info : CombineImprove
Info : 27 elements combined
Info : ImproveMesh
Info : Total badness = 33185.9
Info : Total badness = 29557.2
Info : SplitImprove
Info : badmax = 107.923
Info : 4 splits performed
Info : ImproveMesh
Info : Total badness = 29588.9
Info : Total badness = 29195.3
Info : SwapImprove
Info : 934 swaps performed
Info : SwapImprove2
Info : 0 swaps performed
Info : ImproveMesh
Info : Total badness = 27513.4
Info : Total badness = 26943.9
Info : CombineImprove
Info : 3 elements combined
Info : ImproveMesh
Info : Total badness = 26896.8
Info : Total badness = 26860.6
Info : SplitImprove
Info : badmax = 64.8656
Info : 1 splits performed
Info : ImproveMesh
Info : Total badness = 26867.1
Info : Total badness = 26859.8
Info : SwapImprove
Info : 280 swaps performed
Info : SwapImprove2
Info : 0 swaps performed
Info : ImproveMesh
Info : Total badness = 26625.8
Info : Total badness = 26454.3
Info : CombineImprove
Info : 0 elements combined
Info : ImproveMesh
Info : Total badness = 26454.3
Info : Total badness = 26446.7
Info : SplitImprove
Info : badmax = 60.9791
Info : 0 splits performed
Info : ImproveMesh
Info : Total badness = 26446.7
Info : Total badness = 26445.9
Info : SwapImprove
Info : 105 swaps performed
Info : SwapImprove2
Info : 0 swaps performed
Info : ImproveMesh
Info : Total badness = 26368.2
Info : Total badness = 26301.2
Info : Done optimizing mesh (Wall 0.859175s, CPU 0.860999s)
Info : Writing 'patch_antenna.msh'...
Mesh saved to patch_antenna.mshInfo : Done writing 'patch_antenna.msh'
Nodes: 5094
Elements: 34488
Info : Writing 'patch_antenna.msh'...
Info : Done writing 'patch_antenna.msh'
Mesh visualization#
view_mesh(filename, transparent_groups= "air_sphere__None")
Loading mesh file: patch_antenna.msh
Groups to render transparent: air_sphere__None
Mesh loaded successfully with 2 cell blocks
Found 6786 triangles total
Physical group tags in mesh: {3: 'top_conductor', 4: 'ground_plane', 5: 'lumped_port', 6: 'air_sphere__None', 7: 'air_sphere__substrate'}
Simulation Configuration#
We define the key parameters for the electromagnetic simulation here. These settings control the frequency sweep range, material properties (dielectric constant and loss tangent for the substrate), and solver-specific configurations like port impedance and mesh order.
output_file : output filename for the configuration JSON file
freq_min : minimum frequency for the simulation (GHz)
freq_max: maximum frequency for the simulation (GHz)
freq_step: frequency step for the simulation (GHz)
solver_order: order of the finite element basis functions for the simulation (e.g., 1 for linear, 2 for quadratic)
output_file: str = "patch_antenna.json"
# Sweep de simulación
freq_min: float = 2.5
freq_max: float = 4
freq_step: float = 0.025
solver_order: int = 2
Generating the Palace Configuration File#
Finally, we assemble the simulation parameters into a JSON configuration .
generate_palace_config_from_entities(entity_defs = [e.to_dict() for e in entities],
pg_map = pg_map,
mesh_file = filename,
output_file = 'patch.config',
freq_min = freq_min,
freq_max = freq_max,
freq_step = freq_step ,
L0 = 1.0,
solver_order = solver_order,
absorbing_order = 2,
farfield=True)
Palace config written to patch.config
{'Problem': {'Type': 'Driven', 'Verbose': 2, 'Output': 'postpro/patch'},
'Model': {'Mesh': 'patch_antenna.msh', 'L0': 1.0, 'Refinement': {}},
'Domains': {'Materials': [{'Attributes': [1],
'Permeability': 1.0,
'Permittivity': 1.0,
'LossTan': 0.0},
{'Attributes': [2],
'Permeability': 1.0,
'Permittivity': 2.2,
'LossTan': 0.0009}]},
'Boundaries': {'PEC': {'Attributes': [3, 4]},
'Absorbing': {'Attributes': [6], 'Order': 2},
'LumpedPort': [{'Index': 1,
'Attributes': [5],
'R': 50.0,
'Excitation': True,
'Direction': '+Z'}],
'Postprocessing': {'FarField': {'Attributes': [6], 'NSample': 16000}}},
'Solver': {'Order': 2,
'Device': 'CPU',
'Driven': {'MinFreq': 2.5,
'MaxFreq': 4,
'FreqStep': 0.025,
'SaveStep': 5,
'AdaptiveTol': 0.001},
'Linear': {'Type': 'Default',
'KSPType': 'GMRES',
'Tol': 1e-08,
'MaxIts': 500}}}
Running Palace#
from palacetoolkit.simulation import set_palace_path, run_palace
run_palace(config_file="patch.config", num_procs=16)
Running: /home/martin/.cache/palacetoolkit/runtime/palace-cpu-v0.1.2/bin/palace -np 16 /home/martin/Desktop/PalaceToolkit/docs/examples/patch.config
>> /usr/bin/mpirun -n 16 /home/martin/.cache/palacetoolkit/runtime/palace-cpu-v0.1.2/bin/palace-x86_64.bin /home/martin/Desktop/PalaceToolkit/docs/examples/patch.config
_____________ _______
_____ __ \____ __ /____ ____________
____ /_/ / __ ` / / __ ` / ___/ _ \
___ _____/ /_/ / / /_/ / /__/ ___/
/__/ \___,__/__/\___,__/\_____\_____/
--> Warning!
Output folder is not empty; program will overwrite content! (postpro/patch)
Git changeset ID: v0.16.1-51-g4f2e2d97
Running with 16 MPI processes, 1 OpenMP thread
Device configuration: omp,cpu
Memory configuration: host-std
libCEED backend: /cpu/self/xsmm/blocked
Added 1324 duplicate vertices for interior boundaries in the mesh
Added 3457 duplicate boundary elements for interior boundaries in the mesh
Characteristic length and time scales:
Lc = 1.818e-01 m, tc = 6.065e-01 ns
Finished partitioning mesh into 16 subdomains
Mesh curvature order: 1
Mesh bounding box:
(Xmin, Ymin, Zmin) = (-9.062e-02, -9.058e-02, -9.091e-02) m
(Xmax, Ymax, Zmax) = (+9.091e-02, +9.067e-02, +9.091e-02) m
Parallel Mesh Stats:
minimum average maximum total
vertices 312 401 457 6418
edges 2047 2317 2478 37083
faces 3362 3591 3738 57462
elements 1625 1674 1724 26794
neighbors 3 7 14
minimum maximum
h 0.000933774 0.172125
kappa 1.09793 18.2995
Estimated current per-rank memory usage is: Min. 51.0M, Max. 69.5M, Avg. 53.0M, Total 847.3M
Estimated current per-node memory usage is: Min. 849.4M, Max. 849.4M, Avg. 849.4M, Total 849.4M
Configuring Robin absorbing BC (order 2) at attributes:
6
Configuring Robin impedance BC for lumped ports at attributes:
5: Rs = 7.692e+01 Ω/sq, n = (-1.0,+0.0,+0.0)
Configuring lumped port circuit properties:
Index = 1: R = 5.000e+01 Ω
Configuring lumped port excitation source term at attributes:
5: Index = 1
Configuring Dirichlet PEC BC at attributes:
3-4
Computing adaptive fast frequency response for:
Excitation with index 1 has contributions from:
Lumped port 1
Beginning PROM construction offline phase:
61 points for frequency sweep over [2.500e+00, 4.000e+00] GHz
Assembling system matrices, number of global unknowns:
H1 (p = 2): 43501, ND (p = 2): 189090, RT (p = 2): 252768
Operator assembly level: Partial
Mesh geometries:
Tetrahedron: P = 20, Q = 14 (quadrature order = 4)
Assembling multigrid hierarchy:
Level 0 (p = 1): 37083 unknowns
Level 1 (p = 2): 189090 unknowns
Level 0 (auxiliary) (p = 1): 6418 unknowns
Level 1 (auxiliary) (p = 2): 43501 unknowns
Residual norms for GMRES solve
0 (restart 0) KSP residual norm 3.483989e+01
1 (restart 0) KSP residual norm 1.638033e+01
2 (restart 0) KSP residual norm 1.595283e+01
3 (restart 0) KSP residual norm 6.785846e+00
4 (restart 0) KSP residual norm 6.778450e+00
5 (restart 0) KSP residual norm 3.702500e+00
6 (restart 0) KSP residual norm 3.687719e+00
7 (restart 0) KSP residual norm 2.833579e+00
8 (restart 0) KSP residual norm 2.685200e+00
9 (restart 0) KSP residual norm 2.439460e+00
10 (restart 0) KSP residual norm 2.304808e+00
11 (restart 0) KSP residual norm 2.176711e+00
12 (restart 0) KSP residual norm 2.088950e+00
13 (restart 0) KSP residual norm 1.814150e+00
14 (restart 0) KSP residual norm 1.769837e+00
15 (restart 0) KSP residual norm 1.268215e+00
16 (restart 0) KSP residual norm 1.179278e+00
17 (restart 0) KSP residual norm 9.180005e-01
18 (restart 0) KSP residual norm 8.574307e-01
19 (restart 0) KSP residual norm 7.436316e-01
20 (restart 0) KSP residual norm 7.354207e-01
21 (restart 0) KSP residual norm 6.041496e-01
22 (restart 0) KSP residual norm 5.836149e-01
23 (restart 0) KSP residual norm 4.773363e-01
24 (restart 0) KSP residual norm 4.423789e-01
25 (restart 0) KSP residual norm 3.990211e-01
26 (restart 0) KSP residual norm 3.768231e-01
27 (restart 0) KSP residual norm 3.253256e-01
28 (restart 0) KSP residual norm 3.046586e-01
29 (restart 0) KSP residual norm 2.735369e-01
30 (restart 0) KSP residual norm 2.442329e-01
31 (restart 0) KSP residual norm 2.248002e-01
32 (restart 0) KSP residual norm 1.915834e-01
33 (restart 0) KSP residual norm 1.731497e-01
34 (restart 0) KSP residual norm 1.516500e-01
35 (restart 0) KSP residual norm 1.306338e-01
36 (restart 0) KSP residual norm 1.151003e-01
37 (restart 0) KSP residual norm 1.017698e-01
38 (restart 0) KSP residual norm 8.946518e-02
39 (restart 0) KSP residual norm 8.162207e-02
40 (restart 0) KSP residual norm 6.826053e-02
41 (restart 0) KSP residual norm 5.849272e-02
42 (restart 0) KSP residual norm 4.649408e-02
43 (restart 0) KSP residual norm 3.906652e-02
44 (restart 0) KSP residual norm 3.337561e-02
45 (restart 0) KSP residual norm 2.745105e-02
46 (restart 0) KSP residual norm 2.238034e-02
47 (restart 0) KSP residual norm 1.945662e-02
48 (restart 0) KSP residual norm 1.604033e-02
49 (restart 0) KSP residual norm 1.320134e-02
50 (restart 0) KSP residual norm 1.139103e-02
51 (restart 0) KSP residual norm 9.516884e-03
52 (restart 0) KSP residual norm 7.978735e-03
53 (restart 0) KSP residual norm 6.978859e-03
54 (restart 0) KSP residual norm 6.057595e-03
55 (restart 0) KSP residual norm 5.122472e-03
56 (restart 0) KSP residual norm 4.177217e-03
57 (restart 0) KSP residual norm 3.483511e-03
58 (restart 0) KSP residual norm 2.881101e-03
59 (restart 0) KSP residual norm 2.284306e-03
60 (restart 0) KSP residual norm 1.687449e-03
61 (restart 0) KSP residual norm 1.378651e-03
62 (restart 0) KSP residual norm 1.054077e-03
63 (restart 0) KSP residual norm 8.102737e-04
64 (restart 0) KSP residual norm 5.994272e-04
65 (restart 0) KSP residual norm 4.876721e-04
66 (restart 0) KSP residual norm 3.688129e-04
67 (restart 0) KSP residual norm 2.817588e-04
68 (restart 0) KSP residual norm 2.178700e-04
69 (restart 0) KSP residual norm 1.695158e-04
70 (restart 0) KSP residual norm 1.376695e-04
71 (restart 0) KSP residual norm 1.031975e-04
72 (restart 0) KSP residual norm 7.942367e-05
73 (restart 0) KSP residual norm 6.557393e-05
74 (restart 0) KSP residual norm 5.005595e-05
75 (restart 0) KSP residual norm 3.913512e-05
76 (restart 0) KSP residual norm 3.177019e-05
77 (restart 0) KSP residual norm 2.441544e-05
78 (restart 0) KSP residual norm 1.849384e-05
79 (restart 0) KSP residual norm 1.370196e-05
80 (restart 0) KSP residual norm 1.053222e-05
81 (restart 0) KSP residual norm 8.183339e-06
82 (restart 0) KSP residual norm 6.130604e-06
83 (restart 0) KSP residual norm 4.489035e-06
84 (restart 0) KSP residual norm 3.393996e-06
85 (restart 0) KSP residual norm 2.579677e-06
86 (restart 0) KSP residual norm 1.855782e-06
87 (restart 0) KSP residual norm 1.421381e-06
88 (restart 0) KSP residual norm 1.038339e-06
89 (restart 0) KSP residual norm 7.509084e-07
90 (restart 0) KSP residual norm 5.502241e-07
91 (restart 0) KSP residual norm 4.096127e-07
92 (restart 0) KSP residual norm 3.103170e-07
GMRES solver converged in 92 iterations (avg. reduction factor: 8.175e-01)
Field energy E (9.443e-11 J) + H (8.540e-11 J) = 1.798e-10 J
Residual norms for GMRES solve
0 (restart 0) KSP residual norm 6.127287e+02
1 (restart 0) KSP residual norm 4.133755e+02
2 (restart 0) KSP residual norm 1.524727e+02
3 (restart 0) KSP residual norm 2.562884e+01
4 (restart 0) KSP residual norm 1.342230e+01
5 (restart 0) KSP residual norm 1.209925e+01
6 (restart 0) KSP residual norm 9.415011e+00
7 (restart 0) KSP residual norm 8.309334e+00
8 (restart 0) KSP residual norm 5.956349e+00
9 (restart 0) KSP residual norm 5.499117e+00
10 (restart 0) KSP residual norm 4.871423e+00
11 (restart 0) KSP residual norm 4.446807e+00
12 (restart 0) KSP residual norm 4.323772e+00
13 (restart 0) KSP residual norm 3.666343e+00
14 (restart 0) KSP residual norm 3.346962e+00
15 (restart 0) KSP residual norm 3.037226e+00
16 (restart 0) KSP residual norm 2.860766e+00
17 (restart 0) KSP residual norm 2.484136e+00
18 (restart 0) KSP residual norm 2.303107e+00
19 (restart 0) KSP residual norm 2.050596e+00
20 (restart 0) KSP residual norm 1.934924e+00
21 (restart 0) KSP residual norm 1.720610e+00
22 (restart 0) KSP residual norm 1.519782e+00
23 (restart 0) KSP residual norm 1.440875e+00
24 (restart 0) KSP residual norm 1.287882e+00
25 (restart 0) KSP residual norm 1.107643e+00
26 (restart 0) KSP residual norm 1.025571e+00
27 (restart 0) KSP residual norm 9.424809e-01
28 (restart 0) KSP residual norm 8.875850e-01
29 (restart 0) KSP residual norm 8.041387e-01
30 (restart 0) KSP residual norm 7.352586e-01
31 (restart 0) KSP residual norm 6.196269e-01
32 (restart 0) KSP residual norm 5.701512e-01
33 (restart 0) KSP residual norm 4.908969e-01
34 (restart 0) KSP residual norm 4.713662e-01
35 (restart 0) KSP residual norm 3.834599e-01
36 (restart 0) KSP residual norm 3.166544e-01
37 (restart 0) KSP residual norm 2.843801e-01
38 (restart 0) KSP residual norm 2.341915e-01
39 (restart 0) KSP residual norm 2.028657e-01
40 (restart 0) KSP residual norm 1.830838e-01
41 (restart 0) KSP residual norm 1.527841e-01
42 (restart 0) KSP residual norm 1.386398e-01
43 (restart 0) KSP residual norm 1.189579e-01
44 (restart 0) KSP residual norm 9.824002e-02
45 (restart 0) KSP residual norm 8.667564e-02
46 (restart 0) KSP residual norm 7.410323e-02
47 (restart 0) KSP residual norm 6.769035e-02
48 (restart 0) KSP residual norm 5.549277e-02
49 (restart 0) KSP residual norm 4.946804e-02
50 (restart 0) KSP residual norm 4.226992e-02
51 (restart 0) KSP residual norm 3.536169e-02
52 (restart 0) KSP residual norm 3.194277e-02
53 (restart 0) KSP residual norm 2.479068e-02
54 (restart 0) KSP residual norm 2.107365e-02
55 (restart 0) KSP residual norm 1.667650e-02
56 (restart 0) KSP residual norm 1.350032e-02
57 (restart 0) KSP residual norm 1.097500e-02
58 (restart 0) KSP residual norm 9.149061e-03
59 (restart 0) KSP residual norm 7.239501e-03
60 (restart 0) KSP residual norm 5.479457e-03
61 (restart 0) KSP residual norm 4.315327e-03
62 (restart 0) KSP residual norm 3.204613e-03
63 (restart 0) KSP residual norm 2.504098e-03
64 (restart 0) KSP residual norm 1.951110e-03
65 (restart 0) KSP residual norm 1.456591e-03
66 (restart 0) KSP residual norm 1.081992e-03
67 (restart 0) KSP residual norm 8.312153e-04
68 (restart 0) KSP residual norm 6.614283e-04
69 (restart 0) KSP residual norm 5.144312e-04
70 (restart 0) KSP residual norm 4.159172e-04
71 (restart 0) KSP residual norm 3.222218e-04
72 (restart 0) KSP residual norm 2.523205e-04
73 (restart 0) KSP residual norm 1.931220e-04
74 (restart 0) KSP residual norm 1.470466e-04
75 (restart 0) KSP residual norm 1.212632e-04
76 (restart 0) KSP residual norm 9.132374e-05
77 (restart 0) KSP residual norm 6.646041e-05
78 (restart 0) KSP residual norm 5.102816e-05
79 (restart 0) KSP residual norm 3.905517e-05
80 (restart 0) KSP residual norm 2.732811e-05
81 (restart 0) KSP residual norm 2.035191e-05
82 (restart 0) KSP residual norm 1.629701e-05
83 (restart 0) KSP residual norm 1.241005e-05
84 (restart 0) KSP residual norm 9.646276e-06
85 (restart 0) KSP residual norm 7.234284e-06
86 (restart 0) KSP residual norm 5.387659e-06
GMRES solver converged in 86 iterations (avg. reduction factor: 8.060e-01)
Field energy E (1.791e-10 J) + H (1.403e-10 J) = 3.194e-10 J
Residual norms for GMRES solve
0 (restart 0) KSP residual norm 6.422833e+01
1 (restart 0) KSP residual norm 5.909908e+01
2 (restart 0) KSP residual norm 5.731930e+01
3 (restart 0) KSP residual norm 5.590266e+01
4 (restart 0) KSP residual norm 3.557516e+01
5 (restart 0) KSP residual norm 3.359920e+01
6 (restart 0) KSP residual norm 2.908714e+01
7 (restart 0) KSP residual norm 2.828656e+01
8 (restart 0) KSP residual norm 1.824952e+01
9 (restart 0) KSP residual norm 1.660275e+01
10 (restart 0) KSP residual norm 1.452791e+01
11 (restart 0) KSP residual norm 1.269428e+01
12 (restart 0) KSP residual norm 1.179351e+01
13 (restart 0) KSP residual norm 9.919147e+00
14 (restart 0) KSP residual norm 9.655951e+00
15 (restart 0) KSP residual norm 8.117533e+00
16 (restart 0) KSP residual norm 7.947305e+00
17 (restart 0) KSP residual norm 6.807874e+00
18 (restart 0) KSP residual norm 6.576186e+00
19 (restart 0) KSP residual norm 6.048569e+00
20 (restart 0) KSP residual norm 5.941768e+00
21 (restart 0) KSP residual norm 5.424400e+00
22 (restart 0) KSP residual norm 5.098727e+00
23 (restart 0) KSP residual norm 4.684337e+00
24 (restart 0) KSP residual norm 4.367407e+00
25 (restart 0) KSP residual norm 3.891868e+00
26 (restart 0) KSP residual norm 3.353459e+00
27 (restart 0) KSP residual norm 2.876110e+00
28 (restart 0) KSP residual norm 2.428272e+00
29 (restart 0) KSP residual norm 2.157620e+00
30 (restart 0) KSP residual norm 1.706710e+00
31 (restart 0) KSP residual norm 1.350227e+00
32 (restart 0) KSP residual norm 1.175448e+00
33 (restart 0) KSP residual norm 9.741625e-01
34 (restart 0) KSP residual norm 8.417918e-01
35 (restart 0) KSP residual norm 6.693608e-01
36 (restart 0) KSP residual norm 5.823043e-01
37 (restart 0) KSP residual norm 4.329445e-01
38 (restart 0) KSP residual norm 3.945657e-01
39 (restart 0) KSP residual norm 3.559011e-01
40 (restart 0) KSP residual norm 3.183543e-01
41 (restart 0) KSP residual norm 2.822484e-01
42 (restart 0) KSP residual norm 2.354904e-01
43 (restart 0) KSP residual norm 1.953934e-01
44 (restart 0) KSP residual norm 1.698437e-01
45 (restart 0) KSP residual norm 1.295485e-01
46 (restart 0) KSP residual norm 1.134569e-01
47 (restart 0) KSP residual norm 9.492531e-02
48 (restart 0) KSP residual norm 8.203244e-02
49 (restart 0) KSP residual norm 6.971183e-02
50 (restart 0) KSP residual norm 5.785595e-02
51 (restart 0) KSP residual norm 4.982094e-02
52 (restart 0) KSP residual norm 4.149603e-02
53 (restart 0) KSP residual norm 3.486490e-02
54 (restart 0) KSP residual norm 2.821372e-02
55 (restart 0) KSP residual norm 2.193128e-02
56 (restart 0) KSP residual norm 1.849151e-02
57 (restart 0) KSP residual norm 1.397141e-02
58 (restart 0) KSP residual norm 1.193903e-02
59 (restart 0) KSP residual norm 9.572595e-03
60 (restart 0) KSP residual norm 8.309780e-03
61 (restart 0) KSP residual norm 6.768526e-03
62 (restart 0) KSP residual norm 5.476860e-03
63 (restart 0) KSP residual norm 4.321610e-03
64 (restart 0) KSP residual norm 3.395052e-03
65 (restart 0) KSP residual norm 2.732107e-03
66 (restart 0) KSP residual norm 2.275156e-03
67 (restart 0) KSP residual norm 1.850842e-03
68 (restart 0) KSP residual norm 1.566182e-03
69 (restart 0) KSP residual norm 1.287659e-03
70 (restart 0) KSP residual norm 1.062755e-03
71 (restart 0) KSP residual norm 8.530118e-04
72 (restart 0) KSP residual norm 7.176268e-04
73 (restart 0) KSP residual norm 5.847050e-04
74 (restart 0) KSP residual norm 4.371709e-04
75 (restart 0) KSP residual norm 3.485502e-04
76 (restart 0) KSP residual norm 2.837566e-04
77 (restart 0) KSP residual norm 2.237954e-04
78 (restart 0) KSP residual norm 1.801038e-04
79 (restart 0) KSP residual norm 1.385508e-04
80 (restart 0) KSP residual norm 1.107846e-04
81 (restart 0) KSP residual norm 8.797957e-05
82 (restart 0) KSP residual norm 7.087791e-05
83 (restart 0) KSP residual norm 5.806354e-05
84 (restart 0) KSP residual norm 4.537038e-05
85 (restart 0) KSP residual norm 3.556853e-05
86 (restart 0) KSP residual norm 2.797601e-05
87 (restart 0) KSP residual norm 2.228275e-05
88 (restart 0) KSP residual norm 1.788914e-05
89 (restart 0) KSP residual norm 1.436337e-05
90 (restart 0) KSP residual norm 1.171775e-05
91 (restart 0) KSP residual norm 9.777471e-06
92 (restart 0) KSP residual norm 8.014507e-06
93 (restart 0) KSP residual norm 6.564083e-06
94 (restart 0) KSP residual norm 5.256535e-06
95 (restart 0) KSP residual norm 4.363411e-06
96 (restart 0) KSP residual norm 3.416353e-06
97 (restart 0) KSP residual norm 2.825313e-06
98 (restart 0) KSP residual norm 2.314622e-06
99 (restart 0) KSP residual norm 1.992927e-06
100 (restart 0) KSP residual norm 1.682405e-06
101 (restart 0) KSP residual norm 1.396012e-06
102 (restart 0) KSP residual norm 1.110892e-06
103 (restart 0) KSP residual norm 8.639034e-07
104 (restart 0) KSP residual norm 6.714228e-07
105 (restart 0) KSP residual norm 5.408358e-07
GMRES solver converged in 105 iterations (avg. reduction factor: 8.377e-01)
Greedy iteration 1 (n = 4): ω* = 3.433e+00 GHz (1.308e+01), error = 9.133e-01, memory = 0/2
Field energy E (3.855e-10 J) + H (3.762e-10 J) = 7.617e-10 J
Residual norms for GMRES solve
0 (restart 0) KSP residual norm 6.751877e+01
1 (restart 0) KSP residual norm 6.452576e+01
2 (restart 0) KSP residual norm 6.398192e+01
3 (restart 0) KSP residual norm 6.297234e+01
4 (restart 0) KSP residual norm 5.955310e+01
5 (restart 0) KSP residual norm 5.246780e+01
6 (restart 0) KSP residual norm 5.116704e+01
7 (restart 0) KSP residual norm 4.461565e+01
8 (restart 0) KSP residual norm 3.875282e+01
9 (restart 0) KSP residual norm 3.627986e+01
10 (restart 0) KSP residual norm 3.120721e+01
11 (restart 0) KSP residual norm 3.060050e+01
12 (restart 0) KSP residual norm 2.692292e+01
13 (restart 0) KSP residual norm 2.619024e+01
14 (restart 0) KSP residual norm 2.205613e+01
15 (restart 0) KSP residual norm 2.063419e+01
16 (restart 0) KSP residual norm 1.899624e+01
17 (restart 0) KSP residual norm 1.582685e+01
18 (restart 0) KSP residual norm 1.559804e+01
19 (restart 0) KSP residual norm 1.196281e+01
20 (restart 0) KSP residual norm 1.172514e+01
21 (restart 0) KSP residual norm 9.469576e+00
22 (restart 0) KSP residual norm 8.853273e+00
23 (restart 0) KSP residual norm 7.184457e+00
24 (restart 0) KSP residual norm 5.861032e+00
25 (restart 0) KSP residual norm 5.686578e+00
26 (restart 0) KSP residual norm 4.114097e+00
27 (restart 0) KSP residual norm 3.969076e+00
28 (restart 0) KSP residual norm 3.056252e+00
29 (restart 0) KSP residual norm 2.721980e+00
30 (restart 0) KSP residual norm 2.528253e+00
31 (restart 0) KSP residual norm 2.205267e+00
32 (restart 0) KSP residual norm 2.115015e+00
33 (restart 0) KSP residual norm 1.859324e+00
34 (restart 0) KSP residual norm 1.672388e+00
35 (restart 0) KSP residual norm 1.519707e+00
36 (restart 0) KSP residual norm 1.310987e+00
37 (restart 0) KSP residual norm 1.137148e+00
38 (restart 0) KSP residual norm 9.845613e-01
39 (restart 0) KSP residual norm 8.357532e-01
40 (restart 0) KSP residual norm 7.239113e-01
41 (restart 0) KSP residual norm 6.366858e-01
42 (restart 0) KSP residual norm 5.567867e-01
43 (restart 0) KSP residual norm 4.822652e-01
44 (restart 0) KSP residual norm 4.129331e-01
45 (restart 0) KSP residual norm 3.316254e-01
46 (restart 0) KSP residual norm 2.811233e-01
47 (restart 0) KSP residual norm 2.329883e-01
48 (restart 0) KSP residual norm 1.844688e-01
49 (restart 0) KSP residual norm 1.475320e-01
50 (restart 0) KSP residual norm 1.227750e-01
51 (restart 0) KSP residual norm 1.057340e-01
52 (restart 0) KSP residual norm 9.288955e-02
53 (restart 0) KSP residual norm 7.809988e-02
54 (restart 0) KSP residual norm 6.884301e-02
55 (restart 0) KSP residual norm 5.041672e-02
56 (restart 0) KSP residual norm 4.335446e-02
57 (restart 0) KSP residual norm 3.533921e-02
58 (restart 0) KSP residual norm 3.108481e-02
59 (restart 0) KSP residual norm 2.227216e-02
60 (restart 0) KSP residual norm 1.843009e-02
61 (restart 0) KSP residual norm 1.448048e-02
62 (restart 0) KSP residual norm 1.094719e-02
63 (restart 0) KSP residual norm 8.996505e-03
64 (restart 0) KSP residual norm 6.475258e-03
65 (restart 0) KSP residual norm 5.359283e-03
66 (restart 0) KSP residual norm 4.263527e-03
67 (restart 0) KSP residual norm 3.595564e-03
68 (restart 0) KSP residual norm 2.895906e-03
69 (restart 0) KSP residual norm 2.257061e-03
70 (restart 0) KSP residual norm 1.751555e-03
71 (restart 0) KSP residual norm 1.333477e-03
72 (restart 0) KSP residual norm 1.065507e-03
73 (restart 0) KSP residual norm 8.382675e-04
74 (restart 0) KSP residual norm 6.789414e-04
75 (restart 0) KSP residual norm 5.545764e-04
76 (restart 0) KSP residual norm 4.446536e-04
77 (restart 0) KSP residual norm 3.659269e-04
78 (restart 0) KSP residual norm 2.874459e-04
79 (restart 0) KSP residual norm 2.217447e-04
80 (restart 0) KSP residual norm 1.744376e-04
81 (restart 0) KSP residual norm 1.378919e-04
82 (restart 0) KSP residual norm 1.128298e-04
83 (restart 0) KSP residual norm 8.943913e-05
84 (restart 0) KSP residual norm 6.935279e-05
85 (restart 0) KSP residual norm 5.274236e-05
86 (restart 0) KSP residual norm 3.940963e-05
87 (restart 0) KSP residual norm 2.993260e-05
88 (restart 0) KSP residual norm 2.358713e-05
89 (restart 0) KSP residual norm 1.848710e-05
90 (restart 0) KSP residual norm 1.469989e-05
91 (restart 0) KSP residual norm 1.214209e-05
92 (restart 0) KSP residual norm 9.835470e-06
93 (restart 0) KSP residual norm 8.106071e-06
94 (restart 0) KSP residual norm 6.766851e-06
95 (restart 0) KSP residual norm 5.454406e-06
96 (restart 0) KSP residual norm 4.463527e-06
97 (restart 0) KSP residual norm 3.493510e-06
98 (restart 0) KSP residual norm 2.800834e-06
99 (restart 0) KSP residual norm 2.259994e-06
100 (restart 0) KSP residual norm 1.801515e-06
101 (restart 0) KSP residual norm 1.393576e-06
102 (restart 0) KSP residual norm 1.111101e-06
103 (restart 0) KSP residual norm 8.590819e-07
104 (restart 0) KSP residual norm 6.587193e-07
GMRES solver converged in 104 iterations (avg. reduction factor: 8.375e-01)
Greedy iteration 2 (n = 6): ω* = 3.248e+00 GHz (1.238e+01), error = 2.433e-02, memory = 0/2
Field energy E (1.295e-09 J) + H (1.296e-09 J) = 2.591e-09 J
Residual norms for GMRES solve
0 (restart 0) KSP residual norm 9.177989e+01
1 (restart 0) KSP residual norm 9.152952e+01
2 (restart 0) KSP residual norm 7.869349e+01
3 (restart 0) KSP residual norm 7.424285e+01
4 (restart 0) KSP residual norm 4.169797e+01
5 (restart 0) KSP residual norm 1.598209e+01
6 (restart 0) KSP residual norm 7.376414e+00
7 (restart 0) KSP residual norm 6.229556e+00
8 (restart 0) KSP residual norm 5.932415e+00
9 (restart 0) KSP residual norm 5.135071e+00
10 (restart 0) KSP residual norm 4.850819e+00
11 (restart 0) KSP residual norm 4.568502e+00
12 (restart 0) KSP residual norm 4.091557e+00
13 (restart 0) KSP residual norm 3.834386e+00
14 (restart 0) KSP residual norm 3.181003e+00
15 (restart 0) KSP residual norm 2.959862e+00
16 (restart 0) KSP residual norm 2.657674e+00
17 (restart 0) KSP residual norm 2.428988e+00
18 (restart 0) KSP residual norm 2.149931e+00
19 (restart 0) KSP residual norm 1.900168e+00
20 (restart 0) KSP residual norm 1.703937e+00
21 (restart 0) KSP residual norm 1.592794e+00
22 (restart 0) KSP residual norm 1.311300e+00
23 (restart 0) KSP residual norm 1.237153e+00
24 (restart 0) KSP residual norm 1.008013e+00
25 (restart 0) KSP residual norm 9.098768e-01
26 (restart 0) KSP residual norm 8.476587e-01
27 (restart 0) KSP residual norm 7.151217e-01
28 (restart 0) KSP residual norm 6.442731e-01
29 (restart 0) KSP residual norm 5.336693e-01
30 (restart 0) KSP residual norm 4.878138e-01
31 (restart 0) KSP residual norm 4.065293e-01
32 (restart 0) KSP residual norm 3.789890e-01
33 (restart 0) KSP residual norm 3.092096e-01
34 (restart 0) KSP residual norm 2.952991e-01
35 (restart 0) KSP residual norm 2.565412e-01
36 (restart 0) KSP residual norm 2.431211e-01
37 (restart 0) KSP residual norm 2.101030e-01
38 (restart 0) KSP residual norm 1.977771e-01
39 (restart 0) KSP residual norm 1.786690e-01
40 (restart 0) KSP residual norm 1.638160e-01
41 (restart 0) KSP residual norm 1.493695e-01
42 (restart 0) KSP residual norm 1.337401e-01
43 (restart 0) KSP residual norm 1.225251e-01
44 (restart 0) KSP residual norm 1.081126e-01
45 (restart 0) KSP residual norm 9.973055e-02
46 (restart 0) KSP residual norm 8.744658e-02
47 (restart 0) KSP residual norm 7.199996e-02
48 (restart 0) KSP residual norm 6.361322e-02
49 (restart 0) KSP residual norm 5.272906e-02
50 (restart 0) KSP residual norm 4.331777e-02
51 (restart 0) KSP residual norm 3.485704e-02
52 (restart 0) KSP residual norm 2.680712e-02
53 (restart 0) KSP residual norm 2.252466e-02
54 (restart 0) KSP residual norm 1.844531e-02
55 (restart 0) KSP residual norm 1.534257e-02
56 (restart 0) KSP residual norm 1.193549e-02
57 (restart 0) KSP residual norm 1.020902e-02
58 (restart 0) KSP residual norm 8.386319e-03
59 (restart 0) KSP residual norm 6.919243e-03
60 (restart 0) KSP residual norm 5.730582e-03
61 (restart 0) KSP residual norm 4.833756e-03
62 (restart 0) KSP residual norm 3.986004e-03
63 (restart 0) KSP residual norm 3.130830e-03
64 (restart 0) KSP residual norm 2.569436e-03
65 (restart 0) KSP residual norm 2.007649e-03
66 (restart 0) KSP residual norm 1.603029e-03
67 (restart 0) KSP residual norm 1.319865e-03
68 (restart 0) KSP residual norm 1.093935e-03
69 (restart 0) KSP residual norm 9.393492e-04
70 (restart 0) KSP residual norm 8.067507e-04
71 (restart 0) KSP residual norm 6.841680e-04
72 (restart 0) KSP residual norm 5.682887e-04
73 (restart 0) KSP residual norm 4.560594e-04
74 (restart 0) KSP residual norm 3.691072e-04
75 (restart 0) KSP residual norm 3.072845e-04
76 (restart 0) KSP residual norm 2.590848e-04
77 (restart 0) KSP residual norm 2.211552e-04
78 (restart 0) KSP residual norm 1.850145e-04
79 (restart 0) KSP residual norm 1.570334e-04
80 (restart 0) KSP residual norm 1.356486e-04
81 (restart 0) KSP residual norm 1.119924e-04
82 (restart 0) KSP residual norm 9.190565e-05
83 (restart 0) KSP residual norm 7.025169e-05
84 (restart 0) KSP residual norm 5.594092e-05
85 (restart 0) KSP residual norm 4.305005e-05
86 (restart 0) KSP residual norm 3.489671e-05
87 (restart 0) KSP residual norm 2.882052e-05
88 (restart 0) KSP residual norm 2.376939e-05
89 (restart 0) KSP residual norm 1.997174e-05
90 (restart 0) KSP residual norm 1.648143e-05
91 (restart 0) KSP residual norm 1.284108e-05
92 (restart 0) KSP residual norm 9.620320e-06
93 (restart 0) KSP residual norm 7.278495e-06
94 (restart 0) KSP residual norm 5.806932e-06
95 (restart 0) KSP residual norm 4.891996e-06
96 (restart 0) KSP residual norm 4.221792e-06
97 (restart 0) KSP residual norm 3.448051e-06
98 (restart 0) KSP residual norm 2.803473e-06
99 (restart 0) KSP residual norm 2.230566e-06
100 (restart 0) KSP residual norm 1.749352e-06
101 (restart 0) KSP residual norm 1.476622e-06
102 (restart 0) KSP residual norm 1.180482e-06
103 (restart 0) KSP residual norm 9.567908e-07
104 (restart 0) KSP residual norm 7.251037e-07
GMRES solver converged in 104 iterations (avg. reduction factor: 8.358e-01)
Greedy iteration 3 (n = 8): ω* = 2.924e+00 GHz (1.114e+01), error = 2.067e-02, memory = 0/2
Field energy E (1.804e-10 J) + H (1.451e-10 J) = 3.254e-10 J
Residual norms for GMRES solve
0 (restart 0) KSP residual norm 1.372959e+02
1 (restart 0) KSP residual norm 1.128715e+02
2 (restart 0) KSP residual norm 8.912722e+01
3 (restart 0) KSP residual norm 8.546913e+01
4 (restart 0) KSP residual norm 3.221686e+01
5 (restart 0) KSP residual norm 2.632163e+01
6 (restart 0) KSP residual norm 1.305538e+01
7 (restart 0) KSP residual norm 1.203742e+01
8 (restart 0) KSP residual norm 8.230779e+00
9 (restart 0) KSP residual norm 7.891549e+00
10 (restart 0) KSP residual norm 4.913623e+00
11 (restart 0) KSP residual norm 4.567958e+00
12 (restart 0) KSP residual norm 3.389194e+00
13 (restart 0) KSP residual norm 3.058161e+00
14 (restart 0) KSP residual norm 2.844429e+00
15 (restart 0) KSP residual norm 2.517300e+00
16 (restart 0) KSP residual norm 2.135186e+00
17 (restart 0) KSP residual norm 1.984746e+00
18 (restart 0) KSP residual norm 1.751728e+00
19 (restart 0) KSP residual norm 1.319259e+00
20 (restart 0) KSP residual norm 1.227137e+00
21 (restart 0) KSP residual norm 9.986861e-01
22 (restart 0) KSP residual norm 9.354465e-01
23 (restart 0) KSP residual norm 7.563072e-01
24 (restart 0) KSP residual norm 6.661308e-01
25 (restart 0) KSP residual norm 6.225457e-01
26 (restart 0) KSP residual norm 5.463842e-01
27 (restart 0) KSP residual norm 5.169146e-01
28 (restart 0) KSP residual norm 4.302804e-01
29 (restart 0) KSP residual norm 3.902731e-01
30 (restart 0) KSP residual norm 3.633307e-01
31 (restart 0) KSP residual norm 3.081742e-01
32 (restart 0) KSP residual norm 2.737887e-01
33 (restart 0) KSP residual norm 2.493960e-01
34 (restart 0) KSP residual norm 2.218964e-01
35 (restart 0) KSP residual norm 1.956791e-01
36 (restart 0) KSP residual norm 1.758013e-01
37 (restart 0) KSP residual norm 1.527805e-01
38 (restart 0) KSP residual norm 1.350639e-01
39 (restart 0) KSP residual norm 1.207223e-01
40 (restart 0) KSP residual norm 1.021419e-01
41 (restart 0) KSP residual norm 9.077256e-02
42 (restart 0) KSP residual norm 7.572173e-02
43 (restart 0) KSP residual norm 6.958446e-02
44 (restart 0) KSP residual norm 5.815937e-02
45 (restart 0) KSP residual norm 5.305829e-02
46 (restart 0) KSP residual norm 4.736470e-02
47 (restart 0) KSP residual norm 3.908551e-02
48 (restart 0) KSP residual norm 3.231361e-02
49 (restart 0) KSP residual norm 2.312278e-02
50 (restart 0) KSP residual norm 1.817625e-02
51 (restart 0) KSP residual norm 1.522597e-02
52 (restart 0) KSP residual norm 1.291029e-02
53 (restart 0) KSP residual norm 1.085184e-02
54 (restart 0) KSP residual norm 9.077214e-03
55 (restart 0) KSP residual norm 6.936694e-03
56 (restart 0) KSP residual norm 5.633346e-03
57 (restart 0) KSP residual norm 4.330025e-03
58 (restart 0) KSP residual norm 3.566413e-03
59 (restart 0) KSP residual norm 2.918939e-03
60 (restart 0) KSP residual norm 2.372077e-03
61 (restart 0) KSP residual norm 1.859969e-03
62 (restart 0) KSP residual norm 1.463097e-03
63 (restart 0) KSP residual norm 1.180329e-03
64 (restart 0) KSP residual norm 8.808573e-04
65 (restart 0) KSP residual norm 6.945934e-04
66 (restart 0) KSP residual norm 5.380736e-04
67 (restart 0) KSP residual norm 4.030670e-04
68 (restart 0) KSP residual norm 3.117366e-04
69 (restart 0) KSP residual norm 2.374652e-04
70 (restart 0) KSP residual norm 1.911764e-04
71 (restart 0) KSP residual norm 1.469482e-04
72 (restart 0) KSP residual norm 1.151719e-04
73 (restart 0) KSP residual norm 8.979172e-05
74 (restart 0) KSP residual norm 6.930527e-05
75 (restart 0) KSP residual norm 5.415952e-05
76 (restart 0) KSP residual norm 4.059719e-05
77 (restart 0) KSP residual norm 3.250670e-05
78 (restart 0) KSP residual norm 2.528496e-05
79 (restart 0) KSP residual norm 1.988229e-05
80 (restart 0) KSP residual norm 1.634029e-05
81 (restart 0) KSP residual norm 1.221817e-05
82 (restart 0) KSP residual norm 9.314199e-06
83 (restart 0) KSP residual norm 7.230490e-06
84 (restart 0) KSP residual norm 5.724798e-06
85 (restart 0) KSP residual norm 4.676204e-06
86 (restart 0) KSP residual norm 3.566226e-06
87 (restart 0) KSP residual norm 2.858742e-06
88 (restart 0) KSP residual norm 2.254506e-06
89 (restart 0) KSP residual norm 1.800814e-06
90 (restart 0) KSP residual norm 1.388366e-06
91 (restart 0) KSP residual norm 1.107893e-06
GMRES solver converged in 91 iterations (avg. reduction factor: 8.148e-01)
Greedy iteration 4 (n = 10): ω* = 3.809e+00 GHz (1.451e+01), error = 3.530e-03, memory = 0/2
Field energy E (1.767e-10 J) + H (1.387e-10 J) = 3.154e-10 J
Residual norms for GMRES solve
0 (restart 0) KSP residual norm 6.222085e+01
1 (restart 0) KSP residual norm 4.381337e+01
2 (restart 0) KSP residual norm 3.419550e+01
3 (restart 0) KSP residual norm 2.287002e+01
4 (restart 0) KSP residual norm 1.998795e+01
5 (restart 0) KSP residual norm 1.495055e+01
6 (restart 0) KSP residual norm 1.260422e+01
7 (restart 0) KSP residual norm 6.424551e+00
8 (restart 0) KSP residual norm 5.116454e+00
9 (restart 0) KSP residual norm 4.421058e+00
10 (restart 0) KSP residual norm 3.904571e+00
11 (restart 0) KSP residual norm 3.135637e+00
12 (restart 0) KSP residual norm 2.914152e+00
13 (restart 0) KSP residual norm 2.765510e+00
14 (restart 0) KSP residual norm 2.657584e+00
15 (restart 0) KSP residual norm 2.500346e+00
16 (restart 0) KSP residual norm 2.420276e+00
17 (restart 0) KSP residual norm 2.163025e+00
18 (restart 0) KSP residual norm 2.106579e+00
19 (restart 0) KSP residual norm 1.644889e+00
20 (restart 0) KSP residual norm 1.622478e+00
21 (restart 0) KSP residual norm 1.171059e+00
22 (restart 0) KSP residual norm 1.128753e+00
23 (restart 0) KSP residual norm 8.051986e-01
24 (restart 0) KSP residual norm 6.440209e-01
25 (restart 0) KSP residual norm 5.921281e-01
26 (restart 0) KSP residual norm 4.829806e-01
27 (restart 0) KSP residual norm 4.562400e-01
28 (restart 0) KSP residual norm 3.640074e-01
29 (restart 0) KSP residual norm 3.324961e-01
30 (restart 0) KSP residual norm 2.801600e-01
31 (restart 0) KSP residual norm 2.516290e-01
32 (restart 0) KSP residual norm 2.174024e-01
33 (restart 0) KSP residual norm 1.797887e-01
34 (restart 0) KSP residual norm 1.647001e-01
35 (restart 0) KSP residual norm 1.370087e-01
36 (restart 0) KSP residual norm 1.265886e-01
37 (restart 0) KSP residual norm 1.057798e-01
38 (restart 0) KSP residual norm 9.356038e-02
39 (restart 0) KSP residual norm 8.208251e-02
40 (restart 0) KSP residual norm 7.215524e-02
41 (restart 0) KSP residual norm 6.408075e-02
42 (restart 0) KSP residual norm 5.757803e-02
43 (restart 0) KSP residual norm 5.048022e-02
44 (restart 0) KSP residual norm 4.418607e-02
45 (restart 0) KSP residual norm 4.003496e-02
46 (restart 0) KSP residual norm 3.566512e-02
47 (restart 0) KSP residual norm 3.231030e-02
48 (restart 0) KSP residual norm 2.788927e-02
49 (restart 0) KSP residual norm 2.591259e-02
50 (restart 0) KSP residual norm 2.295406e-02
51 (restart 0) KSP residual norm 2.050630e-02
52 (restart 0) KSP residual norm 1.689337e-02
53 (restart 0) KSP residual norm 1.494613e-02
54 (restart 0) KSP residual norm 1.256695e-02
55 (restart 0) KSP residual norm 1.113618e-02
56 (restart 0) KSP residual norm 8.991409e-03
57 (restart 0) KSP residual norm 7.772763e-03
58 (restart 0) KSP residual norm 6.531004e-03
59 (restart 0) KSP residual norm 5.442527e-03
60 (restart 0) KSP residual norm 4.336628e-03
61 (restart 0) KSP residual norm 3.514321e-03
62 (restart 0) KSP residual norm 2.827697e-03
63 (restart 0) KSP residual norm 2.383514e-03
64 (restart 0) KSP residual norm 1.980419e-03
65 (restart 0) KSP residual norm 1.597098e-03
66 (restart 0) KSP residual norm 1.322080e-03
67 (restart 0) KSP residual norm 1.047992e-03
68 (restart 0) KSP residual norm 8.421180e-04
69 (restart 0) KSP residual norm 6.585459e-04
70 (restart 0) KSP residual norm 5.003593e-04
71 (restart 0) KSP residual norm 3.975060e-04
72 (restart 0) KSP residual norm 3.139329e-04
73 (restart 0) KSP residual norm 2.427717e-04
74 (restart 0) KSP residual norm 1.926201e-04
75 (restart 0) KSP residual norm 1.576160e-04
76 (restart 0) KSP residual norm 1.258398e-04
77 (restart 0) KSP residual norm 9.624037e-05
78 (restart 0) KSP residual norm 8.131621e-05
79 (restart 0) KSP residual norm 6.607089e-05
80 (restart 0) KSP residual norm 4.985662e-05
81 (restart 0) KSP residual norm 3.959006e-05
82 (restart 0) KSP residual norm 3.101511e-05
83 (restart 0) KSP residual norm 2.412430e-05
84 (restart 0) KSP residual norm 2.039786e-05
85 (restart 0) KSP residual norm 1.638222e-05
86 (restart 0) KSP residual norm 1.318017e-05
87 (restart 0) KSP residual norm 1.012080e-05
88 (restart 0) KSP residual norm 7.468368e-06
89 (restart 0) KSP residual norm 5.854505e-06
90 (restart 0) KSP residual norm 4.448338e-06
91 (restart 0) KSP residual norm 3.369989e-06
92 (restart 0) KSP residual norm 2.697929e-06
93 (restart 0) KSP residual norm 2.177307e-06
94 (restart 0) KSP residual norm 1.710142e-06
95 (restart 0) KSP residual norm 1.287683e-06
96 (restart 0) KSP residual norm 9.997472e-07
97 (restart 0) KSP residual norm 7.756246e-07
98 (restart 0) KSP residual norm 5.663468e-07
GMRES solver converged in 98 iterations (avg. reduction factor: 8.278e-01)
Greedy iteration 5 (n = 12): ω* = 2.663e+00 GHz (1.015e+01), error = 3.258e-03, memory = 0/2
Field energy E (1.114e-10 J) + H (9.199e-11 J) = 2.034e-10 J
Residual norms for GMRES solve
0 (restart 0) KSP residual norm 2.535874e+02
1 (restart 0) KSP residual norm 2.490783e+02
2 (restart 0) KSP residual norm 3.652298e+01
3 (restart 0) KSP residual norm 2.500372e+01
4 (restart 0) KSP residual norm 1.623279e+01
5 (restart 0) KSP residual norm 1.600993e+01
6 (restart 0) KSP residual norm 1.246772e+01
7 (restart 0) KSP residual norm 1.129512e+01
8 (restart 0) KSP residual norm 1.070943e+01
9 (restart 0) KSP residual norm 9.127092e+00
10 (restart 0) KSP residual norm 8.847800e+00
11 (restart 0) KSP residual norm 7.922787e+00
12 (restart 0) KSP residual norm 7.387119e+00
13 (restart 0) KSP residual norm 6.780079e+00
14 (restart 0) KSP residual norm 5.392184e+00
15 (restart 0) KSP residual norm 5.286355e+00
16 (restart 0) KSP residual norm 3.935810e+00
17 (restart 0) KSP residual norm 3.771180e+00
18 (restart 0) KSP residual norm 2.974326e+00
19 (restart 0) KSP residual norm 2.909686e+00
20 (restart 0) KSP residual norm 2.443514e+00
21 (restart 0) KSP residual norm 2.348887e+00
22 (restart 0) KSP residual norm 2.014583e+00
23 (restart 0) KSP residual norm 1.969284e+00
24 (restart 0) KSP residual norm 1.713132e+00
25 (restart 0) KSP residual norm 1.649370e+00
26 (restart 0) KSP residual norm 1.319584e+00
27 (restart 0) KSP residual norm 1.256733e+00
28 (restart 0) KSP residual norm 1.041676e+00
29 (restart 0) KSP residual norm 9.532907e-01
30 (restart 0) KSP residual norm 8.586915e-01
31 (restart 0) KSP residual norm 7.226973e-01
32 (restart 0) KSP residual norm 6.201188e-01
33 (restart 0) KSP residual norm 5.630776e-01
34 (restart 0) KSP residual norm 4.817622e-01
35 (restart 0) KSP residual norm 4.265927e-01
36 (restart 0) KSP residual norm 3.588622e-01
37 (restart 0) KSP residual norm 3.107969e-01
38 (restart 0) KSP residual norm 2.785809e-01
39 (restart 0) KSP residual norm 2.407726e-01
40 (restart 0) KSP residual norm 2.126014e-01
41 (restart 0) KSP residual norm 1.768253e-01
42 (restart 0) KSP residual norm 1.425849e-01
43 (restart 0) KSP residual norm 1.223558e-01
44 (restart 0) KSP residual norm 9.900582e-02
45 (restart 0) KSP residual norm 8.679791e-02
46 (restart 0) KSP residual norm 7.461620e-02
47 (restart 0) KSP residual norm 6.444422e-02
48 (restart 0) KSP residual norm 5.567814e-02
49 (restart 0) KSP residual norm 4.760342e-02
50 (restart 0) KSP residual norm 4.190164e-02
51 (restart 0) KSP residual norm 3.400770e-02
52 (restart 0) KSP residual norm 2.941075e-02
53 (restart 0) KSP residual norm 2.316184e-02
54 (restart 0) KSP residual norm 1.968001e-02
55 (restart 0) KSP residual norm 1.589984e-02
56 (restart 0) KSP residual norm 1.366496e-02
57 (restart 0) KSP residual norm 1.085874e-02
58 (restart 0) KSP residual norm 9.196070e-03
59 (restart 0) KSP residual norm 7.616862e-03
60 (restart 0) KSP residual norm 6.400661e-03
61 (restart 0) KSP residual norm 5.392925e-03
62 (restart 0) KSP residual norm 4.158556e-03
63 (restart 0) KSP residual norm 3.487808e-03
64 (restart 0) KSP residual norm 2.720670e-03
65 (restart 0) KSP residual norm 2.400893e-03
66 (restart 0) KSP residual norm 1.966862e-03
67 (restart 0) KSP residual norm 1.708589e-03
68 (restart 0) KSP residual norm 1.402091e-03
69 (restart 0) KSP residual norm 1.160595e-03
70 (restart 0) KSP residual norm 9.375729e-04
71 (restart 0) KSP residual norm 7.682539e-04
72 (restart 0) KSP residual norm 6.433656e-04
73 (restart 0) KSP residual norm 5.561198e-04
74 (restart 0) KSP residual norm 4.668754e-04
75 (restart 0) KSP residual norm 3.863634e-04
76 (restart 0) KSP residual norm 3.161325e-04
77 (restart 0) KSP residual norm 2.422457e-04
78 (restart 0) KSP residual norm 1.896312e-04
79 (restart 0) KSP residual norm 1.457312e-04
80 (restart 0) KSP residual norm 1.144688e-04
81 (restart 0) KSP residual norm 9.605358e-05
82 (restart 0) KSP residual norm 8.294798e-05
83 (restart 0) KSP residual norm 7.070766e-05
84 (restart 0) KSP residual norm 5.852022e-05
85 (restart 0) KSP residual norm 4.708698e-05
86 (restart 0) KSP residual norm 3.903079e-05
87 (restart 0) KSP residual norm 3.174705e-05
88 (restart 0) KSP residual norm 2.567829e-05
89 (restart 0) KSP residual norm 2.031271e-05
90 (restart 0) KSP residual norm 1.580737e-05
91 (restart 0) KSP residual norm 1.270921e-05
92 (restart 0) KSP residual norm 9.942090e-06
93 (restart 0) KSP residual norm 7.824863e-06
94 (restart 0) KSP residual norm 6.289548e-06
95 (restart 0) KSP residual norm 5.075182e-06
96 (restart 0) KSP residual norm 4.010277e-06
97 (restart 0) KSP residual norm 3.164513e-06
98 (restart 0) KSP residual norm 2.518475e-06
GMRES solver converged in 98 iterations (avg. reduction factor: 8.286e-01)
Greedy iteration 6 (n = 14): ω* = 3.025e+00 GHz (1.153e+01), error = 9.695e-04, memory = 1/2
Field energy E (2.621e-10 J) + H (2.210e-10 J) = 4.831e-10 J
Residual norms for GMRES solve
0 (restart 0) KSP residual norm 1.930300e+02
1 (restart 0) KSP residual norm 1.486121e+02
2 (restart 0) KSP residual norm 9.058308e+01
3 (restart 0) KSP residual norm 7.425036e+01
4 (restart 0) KSP residual norm 4.227448e+01
5 (restart 0) KSP residual norm 4.085673e+01
6 (restart 0) KSP residual norm 2.325765e+01
7 (restart 0) KSP residual norm 1.834803e+01
8 (restart 0) KSP residual norm 1.439011e+01
9 (restart 0) KSP residual norm 1.317514e+01
10 (restart 0) KSP residual norm 8.147007e+00
11 (restart 0) KSP residual norm 7.673532e+00
12 (restart 0) KSP residual norm 5.351121e+00
13 (restart 0) KSP residual norm 5.099402e+00
14 (restart 0) KSP residual norm 3.973760e+00
15 (restart 0) KSP residual norm 3.647087e+00
16 (restart 0) KSP residual norm 3.000290e+00
17 (restart 0) KSP residual norm 2.701561e+00
18 (restart 0) KSP residual norm 2.353383e+00
19 (restart 0) KSP residual norm 2.173996e+00
20 (restart 0) KSP residual norm 1.924804e+00
21 (restart 0) KSP residual norm 1.530308e+00
22 (restart 0) KSP residual norm 1.390681e+00
23 (restart 0) KSP residual norm 1.213257e+00
24 (restart 0) KSP residual norm 1.169319e+00
25 (restart 0) KSP residual norm 1.047080e+00
26 (restart 0) KSP residual norm 9.090855e-01
27 (restart 0) KSP residual norm 7.111096e-01
28 (restart 0) KSP residual norm 6.391407e-01
29 (restart 0) KSP residual norm 4.616208e-01
30 (restart 0) KSP residual norm 3.929084e-01
31 (restart 0) KSP residual norm 3.310419e-01
32 (restart 0) KSP residual norm 2.913446e-01
33 (restart 0) KSP residual norm 2.505471e-01
34 (restart 0) KSP residual norm 2.206247e-01
35 (restart 0) KSP residual norm 1.820965e-01
36 (restart 0) KSP residual norm 1.596558e-01
37 (restart 0) KSP residual norm 1.252252e-01
38 (restart 0) KSP residual norm 1.099865e-01
39 (restart 0) KSP residual norm 9.385903e-02
40 (restart 0) KSP residual norm 8.129578e-02
41 (restart 0) KSP residual norm 7.199896e-02
42 (restart 0) KSP residual norm 6.061779e-02
43 (restart 0) KSP residual norm 5.350946e-02
44 (restart 0) KSP residual norm 4.735193e-02
45 (restart 0) KSP residual norm 4.020791e-02
46 (restart 0) KSP residual norm 3.338069e-02
47 (restart 0) KSP residual norm 2.863165e-02
48 (restart 0) KSP residual norm 2.345198e-02
49 (restart 0) KSP residual norm 1.999858e-02
50 (restart 0) KSP residual norm 1.733930e-02
51 (restart 0) KSP residual norm 1.511007e-02
52 (restart 0) KSP residual norm 1.253086e-02
53 (restart 0) KSP residual norm 1.071864e-02
54 (restart 0) KSP residual norm 8.654238e-03
55 (restart 0) KSP residual norm 7.028552e-03
56 (restart 0) KSP residual norm 6.041806e-03
57 (restart 0) KSP residual norm 5.066366e-03
58 (restart 0) KSP residual norm 4.428582e-03
59 (restart 0) KSP residual norm 3.729887e-03
60 (restart 0) KSP residual norm 3.150696e-03
61 (restart 0) KSP residual norm 2.682870e-03
62 (restart 0) KSP residual norm 2.254940e-03
63 (restart 0) KSP residual norm 1.890621e-03
64 (restart 0) KSP residual norm 1.631501e-03
65 (restart 0) KSP residual norm 1.368213e-03
66 (restart 0) KSP residual norm 1.116512e-03
67 (restart 0) KSP residual norm 8.612473e-04
68 (restart 0) KSP residual norm 6.818560e-04
69 (restart 0) KSP residual norm 5.753370e-04
70 (restart 0) KSP residual norm 4.944585e-04
71 (restart 0) KSP residual norm 4.006294e-04
72 (restart 0) KSP residual norm 3.317791e-04
73 (restart 0) KSP residual norm 2.805047e-04
74 (restart 0) KSP residual norm 2.295977e-04
75 (restart 0) KSP residual norm 1.949779e-04
76 (restart 0) KSP residual norm 1.603829e-04
77 (restart 0) KSP residual norm 1.376361e-04
78 (restart 0) KSP residual norm 1.123122e-04
79 (restart 0) KSP residual norm 9.393307e-05
80 (restart 0) KSP residual norm 6.748733e-05
81 (restart 0) KSP residual norm 5.514348e-05
82 (restart 0) KSP residual norm 4.623780e-05
83 (restart 0) KSP residual norm 4.099595e-05
84 (restart 0) KSP residual norm 3.063596e-05
85 (restart 0) KSP residual norm 2.386411e-05
86 (restart 0) KSP residual norm 1.879529e-05
87 (restart 0) KSP residual norm 1.512025e-05
88 (restart 0) KSP residual norm 1.178537e-05
89 (restart 0) KSP residual norm 9.173912e-06
90 (restart 0) KSP residual norm 7.124294e-06
91 (restart 0) KSP residual norm 5.454701e-06
92 (restart 0) KSP residual norm 4.314241e-06
93 (restart 0) KSP residual norm 3.307069e-06
94 (restart 0) KSP residual norm 2.517918e-06
95 (restart 0) KSP residual norm 1.970565e-06
96 (restart 0) KSP residual norm 1.471577e-06
GMRES solver converged in 96 iterations (avg. reduction factor: 8.231e-01)
Greedy iteration 7 (n = 16): ω* = 3.640e+00 GHz (1.387e+01), error = 8.617e-05, memory = 2/2
Field energy E (1.961e-10 J) + H (1.642e-10 J) = 3.603e-10 J
Adaptive sampling converged with 9 frequency samples:
n = 18, error = 8.617e-05, tol = 1.000e-03, memory = 2/2
Sampled frequencies (GHz): 2.500e+00, 4.000e+00, 3.433e+00, 3.248e+00,
2.924e+00, 3.809e+00, 2.663e+00, 3.025e+00,
3.640e+00
Sample errors: inf, inf, 9.133e-01, 2.433e-02, 2.067e-02,
3.530e-03, 3.258e-03, 9.695e-04, 8.617e-05
Total offline phase elapsed time: 7.84e+01 s
Beginning fast frequency sweep online phase
It 1/61: ω/2π = 2.500e+00 GHz (total elapsed time = 7.84e+01 s)
Sol. ||E|| = 3.127238e+01
Field energy E (9.443e-11 J) + H (8.540e-11 J) = 1.798e-10 J
S[1][1] = +9.831e-01-1.419e-01i, |S[1][1]| = -5.890e-02, arg(S[1][1]) = -8.211e+00
Wrote fields to disk (Paraview) at step 1
It 2/61: ω/2π = 2.525e+00 GHz (total elapsed time = 7.95e+01 s)
Sol. ||E|| = 3.154322e+01
Field energy E (9.654e-11 J) + H (8.587e-11 J) = 1.824e-10 J
S[1][1] = +9.783e-01-1.693e-01i, |S[1][1]| = -6.264e-02, arg(S[1][1]) = -9.818e+00
It 3/61: ω/2π = 2.550e+00 GHz (total elapsed time = 8.03e+01 s)
Sol. ||E|| = 3.182459e+01
Field energy E (9.880e-11 J) + H (8.650e-11 J) = 1.853e-10 J
S[1][1] = +9.726e-01-1.970e-01i, |S[1][1]| = -6.676e-02, arg(S[1][1]) = -1.145e+01
It 4/61: ω/2π = 2.575e+00 GHz (total elapsed time = 8.11e+01 s)
Sol. ||E|| = 3.211780e+01
Field energy E (1.012e-10 J) + H (8.732e-11 J) = 1.885e-10 J
S[1][1] = +9.660e-01-2.249e-01i, |S[1][1]| = -7.132e-02, arg(S[1][1]) = -1.311e+01
It 5/61: ω/2π = 2.600e+00 GHz (total elapsed time = 8.20e+01 s)
Sol. ||E|| = 3.242431e+01
Field energy E (1.038e-10 J) + H (8.834e-11 J) = 1.922e-10 J
S[1][1] = +9.584e-01-2.531e-01i, |S[1][1]| = -7.638e-02, arg(S[1][1]) = -1.479e+01
It 6/61: ω/2π = 2.625e+00 GHz (total elapsed time = 8.29e+01 s)
Sol. ||E|| = 3.274585e+01
Field energy E (1.067e-10 J) + H (8.958e-11 J) = 1.962e-10 J
S[1][1] = +9.498e-01-2.815e-01i, |S[1][1]| = -8.202e-02, arg(S[1][1]) = -1.651e+01
Wrote fields to disk (Paraview) at step 6
It 7/61: ω/2π = 2.650e+00 GHz (total elapsed time = 8.42e+01 s)
Sol. ||E|| = 3.308446e+01
Field energy E (1.097e-10 J) + H (9.109e-11 J) = 2.008e-10 J
S[1][1] = +9.400e-01-3.102e-01i, |S[1][1]| = -8.834e-02, arg(S[1][1]) = -1.826e+01
It 8/61: ω/2π = 2.675e+00 GHz (total elapsed time = 8.52e+01 s)
Sol. ||E|| = 3.344253e+01
Field energy E (1.131e-10 J) + H (9.289e-11 J) = 2.060e-10 J
S[1][1] = +9.291e-01-3.393e-01i, |S[1][1]| = -9.545e-02, arg(S[1][1]) = -2.006e+01
It 9/61: ω/2π = 2.700e+00 GHz (total elapsed time = 8.63e+01 s)
Sol. ||E|| = 3.382289e+01
Field energy E (1.168e-10 J) + H (9.503e-11 J) = 2.118e-10 J
S[1][1] = +9.168e-01-3.686e-01i, |S[1][1]| = -1.035e-01, arg(S[1][1]) = -2.190e+01
It 10/61: ω/2π = 2.725e+00 GHz (total elapsed time = 8.74e+01 s)
Sol. ||E|| = 3.422895e+01
Field energy E (1.208e-10 J) + H (9.757e-11 J) = 2.184e-10 J
S[1][1] = +9.032e-01-3.983e-01i, |S[1][1]| = -1.126e-01, arg(S[1][1]) = -2.380e+01
It 11/61: ω/2π = 2.750e+00 GHz (total elapsed time = 8.85e+01 s)
Sol. ||E|| = 3.466481e+01
Field energy E (1.254e-10 J) + H (1.006e-10 J) = 2.259e-10 J
S[1][1] = +8.880e-01-4.284e-01i, |S[1][1]| = -1.231e-01, arg(S[1][1]) = -2.576e+01
Wrote fields to disk (Paraview) at step 11
It 12/61: ω/2π = 2.775e+00 GHz (total elapsed time = 9.00e+01 s)
Sol. ||E|| = 3.513547e+01
Field energy E (1.304e-10 J) + H (1.041e-10 J) = 2.345e-10 J
S[1][1] = +8.711e-01-4.589e-01i, |S[1][1]| = -1.351e-01, arg(S[1][1]) = -2.778e+01
It 13/61: ω/2π = 2.800e+00 GHz (total elapsed time = 9.12e+01 s)
Sol. ||E|| = 3.564703e+01
Field energy E (1.362e-10 J) + H (1.083e-10 J) = 2.445e-10 J
S[1][1] = +8.523e-01-4.898e-01i, |S[1][1]| = -1.490e-01, arg(S[1][1]) = -2.988e+01
It 14/61: ω/2π = 2.825e+00 GHz (total elapsed time = 9.24e+01 s)
Sol. ||E|| = 3.620704e+01
Field energy E (1.427e-10 J) + H (1.133e-10 J) = 2.560e-10 J
S[1][1] = +8.313e-01-5.211e-01i, |S[1][1]| = -1.654e-01, arg(S[1][1]) = -3.208e+01
It 15/61: ω/2π = 2.850e+00 GHz (total elapsed time = 9.37e+01 s)
Sol. ||E|| = 3.682492e+01
Field energy E (1.501e-10 J) + H (1.193e-10 J) = 2.694e-10 J
S[1][1] = +8.079e-01-5.528e-01i, |S[1][1]| = -1.846e-01, arg(S[1][1]) = -3.438e+01
It 16/61: ω/2π = 2.875e+00 GHz (total elapsed time = 9.50e+01 s)
Sol. ||E|| = 3.751249e+01
Field energy E (1.588e-10 J) + H (1.264e-10 J) = 2.852e-10 J
S[1][1] = +7.817e-01-5.850e-01i, |S[1][1]| = -2.074e-01, arg(S[1][1]) = -3.681e+01
Wrote fields to disk (Paraview) at step 16
It 17/61: ω/2π = 2.900e+00 GHz (total elapsed time = 9.67e+01 s)
Sol. ||E|| = 3.828480e+01
Field energy E (1.689e-10 J) + H (1.350e-10 J) = 3.040e-10 J
S[1][1] = +7.523e-01-6.176e-01i, |S[1][1]| = -2.350e-01, arg(S[1][1]) = -3.939e+01
It 18/61: ω/2π = 2.925e+00 GHz (total elapsed time = 9.82e+01 s)
Sol. ||E|| = 3.916146e+01
Field energy E (1.810e-10 J) + H (1.456e-10 J) = 3.265e-10 J
S[1][1] = +7.189e-01-6.505e-01i, |S[1][1]| = -2.685e-01, arg(S[1][1]) = -4.214e+01
It 19/61: ω/2π = 2.950e+00 GHz (total elapsed time = 9.96e+01 s)
Sol. ||E|| = 4.016750e+01
Field energy E (1.954e-10 J) + H (1.585e-10 J) = 3.539e-10 J
S[1][1] = +6.810e-01-6.837e-01i, |S[1][1]| = -3.098e-01, arg(S[1][1]) = -4.511e+01
It 20/61: ω/2π = 2.975e+00 GHz (total elapsed time = 1.01e+02 s)
Sol. ||E|| = 4.133465e+01
Field energy E (2.130e-10 J) + H (1.746e-10 J) = 3.876e-10 J
S[1][1] = +6.375e-01-7.167e-01i, |S[1][1]| = -3.616e-01, arg(S[1][1]) = -4.835e+01
It 21/61: ω/2π = 3.000e+00 GHz (total elapsed time = 1.03e+02 s)
Sol. ||E|| = 4.270686e+01
Field energy E (2.347e-10 J) + H (1.950e-10 J) = 4.297e-10 J
S[1][1] = +5.872e-01-7.493e-01i, |S[1][1]| = -4.276e-01, arg(S[1][1]) = -5.192e+01
Wrote fields to disk (Paraview) at step 21
It 22/61: ω/2π = 3.025e+00 GHz (total elapsed time = 1.05e+02 s)
Sol. ||E|| = 4.434163e+01
Field energy E (2.621e-10 J) + H (2.210e-10 J) = 4.832e-10 J
S[1][1] = +5.284e-01-7.806e-01i, |S[1][1]| = -5.135e-01, arg(S[1][1]) = -5.591e+01
It 23/61: ω/2π = 3.050e+00 GHz (total elapsed time = 1.06e+02 s)
Sol. ||E|| = 4.631569e+01
Field energy E (2.972e-10 J) + H (2.549e-10 J) = 5.521e-10 J
S[1][1] = +4.589e-01-8.092e-01i, |S[1][1]| = -6.278e-01, arg(S[1][1]) = -6.044e+01
It 24/61: ω/2π = 3.075e+00 GHz (total elapsed time = 1.08e+02 s)
Sol. ||E|| = 4.873113e+01
Field energy E (3.429e-10 J) + H (2.998e-10 J) = 6.427e-10 J
S[1][1] = +3.760e-01-8.328e-01i, |S[1][1]| = -7.838e-01, arg(S[1][1]) = -6.570e+01
It 25/61: ω/2π = 3.100e+00 GHz (total elapsed time = 1.10e+02 s)
Sol. ||E|| = 5.172111e+01
Field energy E (4.038e-10 J) + H (3.603e-10 J) = 7.640e-10 J
S[1][1] = +2.761e-01-8.470e-01i, |S[1][1]| = -1.004e+00, arg(S[1][1]) = -7.195e+01
It 26/61: ω/2π = 3.125e+00 GHz (total elapsed time = 1.12e+02 s)
Sol. ||E|| = 5.544988e+01
Field energy E (4.860e-10 J) + H (4.430e-10 J) = 9.290e-10 J
S[1][1] = +1.555e-01-8.445e-01i, |S[1][1]| = -1.324e+00, arg(S[1][1]) = -7.957e+01
Wrote fields to disk (Paraview) at step 26
It 27/61: ω/2π = 3.150e+00 GHz (total elapsed time = 1.14e+02 s)
Sol. ||E|| = 6.009117e+01
Field energy E (5.981e-10 J) + H (5.571e-10 J) = 1.155e-09 J
S[1][1] = +1.151e-02-8.119e-01i, |S[1][1]| = -1.809e+00, arg(S[1][1]) = -8.919e+01
It 28/61: ω/2π = 3.175e+00 GHz (total elapsed time = 1.16e+02 s)
Sol. ||E|| = 6.574242e+01
Field energy E (7.492e-10 J) + H (7.127e-10 J) = 1.462e-09 J
S[1][1] = -1.524e-01-7.277e-01i, |S[1][1]| = -2.574e+00, arg(S[1][1]) = -1.018e+02
It 29/61: ω/2π = 3.200e+00 GHz (total elapsed time = 1.17e+02 s)
Sol. ||E|| = 7.218857e+01
Field energy E (9.417e-10 J) + H (9.137e-10 J) = 1.855e-09 J
S[1][1] = -3.152e-01-5.617e-01i, |S[1][1]| = -3.821e+00, arg(S[1][1]) = -1.193e+02
It 30/61: ω/2π = 3.225e+00 GHz (total elapsed time = 1.19e+02 s)
Sol. ||E|| = 7.844610e+01
Field energy E (1.151e-09 J) + H (1.137e-09 J) = 2.288e-09 J
S[1][1] = -4.198e-01-2.915e-01i, |S[1][1]| = -5.830e+00, arg(S[1][1]) = -1.452e+02
It 31/61: ω/2π = 3.250e+00 GHz (total elapsed time = 1.21e+02 s)
Sol. ||E|| = 8.244404e+01
Field energy E (1.303e-09 J) + H (1.305e-09 J) = 2.608e-09 J
S[1][1] = -3.766e-01+4.828e-02i, |S[1][1]| = -8.411e+00, arg(S[1][1]) = +1.727e+02
Wrote fields to disk (Paraview) at step 31
It 32/61: ω/2π = 3.275e+00 GHz (total elapsed time = 1.24e+02 s)
Sol. ||E|| = 8.204990e+01
Field energy E (1.305e-09 J) + H (1.321e-09 J) = 2.626e-09 J
S[1][1] = -1.447e-01+3.319e-01i, |S[1][1]| = -8.825e+00, arg(S[1][1]) = +1.136e+02
It 33/61: ω/2π = 3.300e+00 GHz (total elapsed time = 1.26e+02 s)
Sol. ||E|| = 7.731434e+01
Field energy E (1.155e-09 J) + H (1.176e-09 J) = 2.331e-09 J
S[1][1] = +1.838e-01+4.414e-01i, |S[1][1]| = -6.409e+00, arg(S[1][1]) = +6.739e+01
It 34/61: ω/2π = 3.325e+00 GHz (total elapsed time = 1.28e+02 s)
Sol. ||E|| = 7.049695e+01
Field energy E (9.430e-10 J) + H (9.616e-10 J) = 1.905e-09 J
S[1][1] = +4.739e-01+3.874e-01i, |S[1][1]| = -4.264e+00, arg(S[1][1]) = +3.926e+01
It 35/61: ω/2π = 3.350e+00 GHz (total elapsed time = 1.30e+02 s)
Sol. ||E|| = 6.376662e+01
Field energy E (7.481e-10 J) + H (7.601e-10 J) = 1.508e-09 J
S[1][1] = +6.699e-01+2.525e-01i, |S[1][1]| = -2.903e+00, arg(S[1][1]) = +2.066e+01
It 36/61: ω/2π = 3.375e+00 GHz (total elapsed time = 1.32e+02 s)
Sol. ||E|| = 5.811103e+01
Field energy E (5.964e-10 J) + H (6.011e-10 J) = 1.198e-09 J
S[1][1] = +7.821e-01+1.002e-01i, |S[1][1]| = -2.064e+00, arg(S[1][1]) = +7.300e+00
Wrote fields to disk (Paraview) at step 36
It 37/61: ω/2π = 3.400e+00 GHz (total elapsed time = 1.35e+02 s)
Sol. ||E|| = 5.369081e+01
Field energy E (4.855e-10 J) + H (4.835e-10 J) = 9.691e-10 J
S[1][1] = +8.372e-01-4.174e-02i, |S[1][1]| = -1.533e+00, arg(S[1][1]) = -2.854e+00
It 38/61: ω/2π = 3.425e+00 GHz (total elapsed time = 1.37e+02 s)
Sol. ||E|| = 5.034358e+01
Field energy E (4.057e-10 J) + H (3.980e-10 J) = 8.037e-10 J
S[1][1] = +8.570e-01-1.655e-01i, |S[1][1]| = -1.182e+00, arg(S[1][1]) = -1.093e+01
It 39/61: ω/2π = 3.450e+00 GHz (total elapsed time = 1.39e+02 s)
Sol. ||E|| = 4.784135e+01
Field energy E (3.480e-10 J) + H (3.355e-10 J) = 6.835e-10 J
S[1][1] = +8.553e-01-2.712e-01i, |S[1][1]| = -9.412e-01, arg(S[1][1]) = -1.759e+01
It 40/61: ω/2π = 3.475e+00 GHz (total elapsed time = 1.41e+02 s)
Sol. ||E|| = 4.598016e+01
Field energy E (3.058e-10 J) + H (2.892e-10 J) = 5.950e-10 J
S[1][1] = +8.407e-01-3.615e-01i, |S[1][1]| = -7.708e-01, arg(S[1][1]) = -2.327e+01
It 41/61: ω/2π = 3.500e+00 GHz (total elapsed time = 1.44e+02 s)
Sol. ||E|| = 4.459951e+01
Field energy E (2.744e-10 J) + H (2.545e-10 J) = 5.289e-10 J
S[1][1] = +8.179e-01-4.391e-01i, |S[1][1]| = -6.464e-01, arg(S[1][1]) = -2.823e+01
Wrote fields to disk (Paraview) at step 41
It 42/61: ω/2π = 3.525e+00 GHz (total elapsed time = 1.47e+02 s)
Sol. ||E|| = 4.357915e+01
Field energy E (2.509e-10 J) + H (2.280e-10 J) = 4.788e-10 J
S[1][1] = +7.899e-01-5.064e-01i, |S[1][1]| = -5.534e-01, arg(S[1][1]) = -3.266e+01
It 43/61: ω/2π = 3.550e+00 GHz (total elapsed time = 1.49e+02 s)
Sol. ||E|| = 4.283053e+01
Field energy E (2.329e-10 J) + H (2.076e-10 J) = 4.405e-10 J
S[1][1] = +7.584e-01-5.654e-01i, |S[1][1]| = -4.823e-01, arg(S[1][1]) = -3.670e+01
It 44/61: ω/2π = 3.575e+00 GHz (total elapsed time = 1.52e+02 s)
Sol. ||E|| = 4.228870e+01
Field energy E (2.191e-10 J) + H (1.916e-10 J) = 4.107e-10 J
S[1][1] = +7.246e-01-6.175e-01i, |S[1][1]| = -4.271e-01, arg(S[1][1]) = -4.044e+01
It 45/61: ω/2π = 3.600e+00 GHz (total elapsed time = 1.54e+02 s)
Sol. ||E|| = 4.190578e+01
Field energy E (2.084e-10 J) + H (1.791e-10 J) = 3.875e-10 J
S[1][1] = +6.889e-01-6.640e-01i, |S[1][1]| = -3.836e-01, arg(S[1][1]) = -4.394e+01
It 46/61: ω/2π = 3.625e+00 GHz (total elapsed time = 1.57e+02 s)
Sol. ||E|| = 4.164629e+01
Field energy E (2.001e-10 J) + H (1.691e-10 J) = 3.692e-10 J
S[1][1] = +6.519e-01-7.056e-01i, |S[1][1]| = -3.489e-01, arg(S[1][1]) = -4.727e+01
Wrote fields to disk (Paraview) at step 46
It 47/61: ω/2π = 3.650e+00 GHz (total elapsed time = 1.60e+02 s)
Sol. ||E|| = 4.148362e+01
Field energy E (1.936e-10 J) + H (1.612e-10 J) = 3.548e-10 J
S[1][1] = +6.137e-01-7.431e-01i, |S[1][1]| = -3.210e-01, arg(S[1][1]) = -5.045e+01
It 48/61: ω/2π = 3.675e+00 GHz (total elapsed time = 1.63e+02 s)
Sol. ||E|| = 4.139766e+01
Field energy E (1.886e-10 J) + H (1.550e-10 J) = 3.436e-10 J
S[1][1] = +5.745e-01-7.769e-01i, |S[1][1]| = -2.983e-01, arg(S[1][1]) = -5.352e+01
It 49/61: ω/2π = 3.700e+00 GHz (total elapsed time = 1.65e+02 s)
Sol. ||E|| = 4.137299e+01
Field energy E (1.847e-10 J) + H (1.500e-10 J) = 3.347e-10 J
S[1][1] = +5.344e-01-8.074e-01i, |S[1][1]| = -2.799e-01, arg(S[1][1]) = -5.650e+01
It 50/61: ω/2π = 3.725e+00 GHz (total elapsed time = 1.68e+02 s)
Sol. ||E|| = 4.139769e+01
Field energy E (1.818e-10 J) + H (1.461e-10 J) = 3.279e-10 J
S[1][1] = +4.935e-01-8.350e-01i, |S[1][1]| = -2.648e-01, arg(S[1][1]) = -5.942e+01
It 51/61: ω/2π = 3.750e+00 GHz (total elapsed time = 1.71e+02 s)
Sol. ||E|| = 4.146243e+01
Field energy E (1.796e-10 J) + H (1.431e-10 J) = 3.227e-10 J
S[1][1] = +4.518e-01-8.599e-01i, |S[1][1]| = -2.524e-01, arg(S[1][1]) = -6.228e+01
Wrote fields to disk (Paraview) at step 51
It 52/61: ω/2π = 3.775e+00 GHz (total elapsed time = 1.74e+02 s)
Sol. ||E|| = 4.155978e+01
Field energy E (1.780e-10 J) + H (1.408e-10 J) = 3.188e-10 J
S[1][1] = +4.094e-01-8.821e-01i, |S[1][1]| = -2.422e-01, arg(S[1][1]) = -6.510e+01
It 53/61: ω/2π = 3.800e+00 GHz (total elapsed time = 1.77e+02 s)
Sol. ||E|| = 4.168380e+01
Field energy E (1.769e-10 J) + H (1.392e-10 J) = 3.161e-10 J
S[1][1] = +3.662e-01-9.019e-01i, |S[1][1]| = -2.339e-01, arg(S[1][1]) = -6.790e+01
It 54/61: ω/2π = 3.825e+00 GHz (total elapsed time = 1.80e+02 s)
Sol. ||E|| = 4.182965e+01
Field energy E (1.763e-10 J) + H (1.380e-10 J) = 3.143e-10 J
S[1][1] = +3.223e-01-9.193e-01i, |S[1][1]| = -2.272e-01, arg(S[1][1]) = -7.068e+01
It 55/61: ω/2π = 3.850e+00 GHz (total elapsed time = 1.83e+02 s)
Sol. ||E|| = 4.199333e+01
Field energy E (1.760e-10 J) + H (1.374e-10 J) = 3.134e-10 J
S[1][1] = +2.777e-01-9.344e-01i, |S[1][1]| = -2.218e-01, arg(S[1][1]) = -7.345e+01
It 56/61: ω/2π = 3.875e+00 GHz (total elapsed time = 1.86e+02 s)
Sol. ||E|| = 4.217152e+01
Field energy E (1.760e-10 J) + H (1.371e-10 J) = 3.131e-10 J
S[1][1] = +2.324e-01-9.472e-01i, |S[1][1]| = -2.175e-01, arg(S[1][1]) = -7.622e+01
Wrote fields to disk (Paraview) at step 56
It 57/61: ω/2π = 3.900e+00 GHz (total elapsed time = 1.89e+02 s)
Sol. ||E|| = 4.236137e+01
Field energy E (1.763e-10 J) + H (1.372e-10 J) = 3.135e-10 J
S[1][1] = +1.865e-01-9.577e-01i, |S[1][1]| = -2.142e-01, arg(S[1][1]) = -7.898e+01
It 58/61: ω/2π = 3.925e+00 GHz (total elapsed time = 1.92e+02 s)
Sol. ||E|| = 4.256043e+01
Field energy E (1.768e-10 J) + H (1.376e-10 J) = 3.144e-10 J
S[1][1] = +1.400e-01-9.658e-01i, |S[1][1]| = -2.117e-01, arg(S[1][1]) = -8.175e+01
It 59/61: ω/2π = 3.950e+00 GHz (total elapsed time = 1.95e+02 s)
Sol. ||E|| = 4.276658e+01
Field energy E (1.774e-10 J) + H (1.383e-10 J) = 3.157e-10 J
S[1][1] = +9.293e-02-9.717e-01i, |S[1][1]| = -2.100e-01, arg(S[1][1]) = -8.454e+01
It 60/61: ω/2π = 3.975e+00 GHz (total elapsed time = 1.98e+02 s)
Sol. ||E|| = 4.297789e+01
Field energy E (1.782e-10 J) + H (1.392e-10 J) = 3.174e-10 J
S[1][1] = +4.541e-02-9.752e-01i, |S[1][1]| = -2.088e-01, arg(S[1][1]) = -8.733e+01
It 61/61: ω/2π = 4.000e+00 GHz (total elapsed time = 2.02e+02 s)
Sol. ||E|| = 4.319265e+01
Field energy E (1.791e-10 J) + H (1.403e-10 J) = 3.194e-10 J
S[1][1] = -2.519e-03-9.763e-01i, |S[1][1]| = -2.082e-01, arg(S[1][1]) = -9.015e+01
Wrote fields to disk (Paraview) at step 61
Completed 0 iterations of adaptive mesh refinement (AMR):
Indicator norm = 1.328e-01, global unknowns = 189090
Max. iterations = 0, tol. = 1.000e-02
Estimated peak per-rank memory usage is: Min. 172.6M, Max. 682.4M, Avg. 209.3M, Total 3.3G
Estimated peak per-node memory usage is: Min. 3.3G, Max. 3.3G, Avg. 3.3G, Total 3.3G
Elapsed Time Report (s) Min. Max. Avg.
==============================================================
Initialization 0.035 0.116 0.109
Mesh Preprocessing 0.067 0.141 0.071
Operator Construction 0.450 60.657 56.887
Linear Solve 8.382 8.548 8.413
Setup 3.987 3.988 3.988
Preconditioner 57.619 58.089 58.026
Coarse Solve 4.493 4.822 4.534
PROM Construction 0.142 0.147 0.143
PROM Solve 0.011 0.012 0.011
Estimation 0.047 0.052 0.050
Construction 0.300 0.301 0.300
Solve 3.153 3.156 3.154
Postprocessing 0.454 76.883 5.232
Far Fields 44.855 44.868 44.861
Paraview 4.867 21.089 20.074
Disk IO 0.081 0.082 0.082
--------------------------------------------------------------
Total 206.296 206.316 206.307
Peak Memory Per-Node Total Total HWM
==============================================================
Initialization 76.8M 76.8M 76.8M
Mesh Preprocessing 59.8M 59.8M 136.6M
Operator Construction 150.9M 150.9M 287.6M
Linear Solve 2.1M 2.1M 289.7M
Setup 525.7M 525.7M 815.4M
Preconditioner 13.9M 13.9M 829.3M
Coarse Solve 1.1G 1.1G 1.9G
PROM Construction 0.0K 0.0K 1.9G
PROM Solve 520.0K 520.0K 1.9G
Estimation 6.2M 6.2M 1.9G
Construction 222.9M 222.9M 2.1G
Solve 256.0K 256.0K 2.1G
Postprocessing 495.1M 495.1M 2.6G
Far Fields 0.0K 0.0K 2.6G
Paraview 2.2M 2.2M 2.6G
Disk IO 11.2M 11.2M 2.6G
--------------------------------------------------------------
Total 2.9G 2.9G 2.9G
Post processing.#
We want to see the S parameters, H plane, E plane and the radiation pattern.
# S parameters. Return the frequency where the minimum is reached.
from pathlib import Path
notebook_dir = Path().resolve()
postpro_dir = notebook_dir / "postpro" / "patch"
f = s_params(str(postpro_dir / "port-S.csv"))
Additional Field Visualizations at Resonant Frequency f#
The next two views use the new VTU workflow:
Surface-current-oriented view over antenna conductors.
A z-slice in the air region above the patch to inspect forward propagation.
import importlib
import pyvista as pv
import palacetoolkit.postpro_vtu as postpro_vtu
postpro_vtu = importlib.reload(postpro_vtu)
# Prefer interactive backends in notebooks.
pv_backend = "static"
for candidate in ("trame", "client", "server"):
try:
pv.set_jupyter_backend(candidate)
pv_backend = candidate
break
except Exception:
pass
# Synchronize boundary/volume steps to the solved frequency f.
boundary_step, volume_step = postpro_vtu.resolve_synced_step_indices(
postpro_dir,
boundary_dataset="driven_boundary",
volume_dataset="driven",
timestep=float(f),
)
selector_ctx = postpro_vtu.build_selector_context("patch.config", pg_map)
conductors = ["top_conductor", "ground_plane"]
boundary_fields = postpro_vtu.load_boundary_field_data(
postpro_dir,
selector_ctx,
entity_names=conductors,
dataset_name="driven_boundary",
step_index=boundary_step,
)
# Prefer explicit current-like vectors when present.
surface_vector_candidates = ["Jsurf_real", "J_real", "Jsurf", "J", "K_real", "K", "H_real", "E_real", "S"]
available_boundary = set(boundary_fields.point_arrays)
surface_vector = next((name for name in surface_vector_candidates if name in available_boundary), None)
if surface_vector is None:
raise KeyError(f"No suitable surface vector field found. Available: {sorted(available_boundary)}")
pl_surface = postpro_vtu.plot_boundary_field(
boundary_fields,
vector_field=surface_vector,
component="mag",
cmap="plasma",
log_scale=True,
opacity=0.82,
scalar_bar_title=f"|{surface_vector}| on conductors @ {float(f):.3f} GHz",
show_edges=False,
off_screen=False,
)
# Improve transparency sorting when available.
try:
pl_surface.enable_depth_peeling()
except Exception:
pass
# Keep a subtle wireframe so the surface crowding remains visible.
# pl_surface.add_mesh(
# boundary_fields.mesh,
# style="wireframe",
# color="white",
# line_width=1.0,
# opacity=0.40,
# lighting=True,
# )
# Orthographic top view with axis alignment.
top_view = True
if top_view:
bounds = boundary_fields.mesh.bounds
cx = 0.5 * (bounds[0] + bounds[1])
cy = 0.5 * (bounds[2] + bounds[3])
cz = 0.5 * (bounds[4] + bounds[5])
span_xy = max(bounds[1] - bounds[0], bounds[3] - bounds[2])
cam_dist = max(span_xy, 1e-9) * 3.0
pl_surface.camera.position = (cx, cy, cz + cam_dist)
pl_surface.camera.focal_point = (cx, cy, cz)
pl_surface.camera.up = (0.0, 1.0, 0.0)
pl_surface.enable_parallel_projection()
pl_surface.camera.parallel_scale = 0.6 * span_xy
pl_surface.add_bounding_box(color="black", line_width=1.0)
pl_surface.show(jupyter_backend=pv_backend)
from palacetoolkit.postpro_vtu import (
activate_vector_component,
extract_axis_slice,
load_volume_field_data,
)
# Load volume data at the synchronized frequency step.
volume_fields = load_volume_field_data(
postpro_dir,
dataset_name="driven",
step_index=volume_step,
)
# Slice slightly above the patch into the air region, along forward radiation direction (+z).
z_air_slice = h + 0.10 * wavelength
slice_mesh = extract_axis_slice(volume_fields, axis="z", value=float(z_air_slice))
scalar_name = activate_vector_component(slice_mesh, field_name="S", component="z", output_name="S_z")
# Combine mesh geometry + semi-transparent volume slice in one scene.
mesh_geom = pv.read(filename)
pl_air_slice = pv.Plotter(off_screen=False)
pl_air_slice.set_background("white")
# Keep a subtle wireframe so the surface crowding remains visible.
pl_air_slice.add_mesh(
boundary_fields.mesh,
style="wireframe",
color="black",
line_width=1.0,
opacity=0.25,
lighting=True,
)
# Overlay the slice with alpha transparency.
pl_air_slice.add_mesh(
slice_mesh,
scalars=scalar_name,
cmap="viridis",
opacity=0.62,
show_edges=False,
scalar_bar_args={"title": f"S_z in air slice @ z={z_air_slice:.4f} m, f={float(f):.3f} GHz"},
)
pl_air_slice.add_axes()
pl_air_slice.camera_position = "iso"
pl_air_slice.show(jupyter_backend=pv_backend)
data, label = load_data(str(postpro_dir / "farfield-rE.csv"), f)
polar_plots(data, label)
# Radiation pattern.
three_d_plot(
data,
label,
n_theta = 360,
n_phi = 720,
n_smooth = 100,
taubin_pass_band = 0.1,
)