Monopole Antenna

Monopole Antenna¶

We are going to modify the code of the dipole antenna to create a monopole antenna. The monopole antenna is a half of the dipole antenna, and it is typically mounted above a ground plane.

In [1]:

import gmsh
import math
import os

from palacetoolkit.geometry import (xmin, xmax, ymin, ymax, zmin, zmax, extract_tag)
from palacetoolkit.viz import view_mesh
from palacetoolkit.mesh import (
    Entity, 
    run_meshing_pipeline, 
    generate_3d_mesh, 
    refine_near_surfaces
)

import gmsh import math import os from palacetoolkit.geometry import (xmin, xmax, ymin, ymax, zmin, zmax, extract_tag) from palacetoolkit.viz import view_mesh from palacetoolkit.mesh import ( Entity, run_meshing_pipeline, generate_3d_mesh, refine_near_surfaces )

Parameters:

• filename - Output mesh filename
• wavelength - Wavelength of the resulting electromagnetic wave
• arm_length - Length of each antenna arm (default: wavelength/4)
• arm_radius - Radius of the cylindrical antenna arms (default: arm_length/20)
• base_length - Length of the ground plane (default: arm_radius * 4)
• base_width - Width of the ground plane (default: arm_radius * 4)
• gap_size - Size of the gap between the two arms (port region) (default: arm_length/100)
• outer_boundary_radius - Radius of the outer spherical boundary (default: 1.5*wavelength)
• verbose - Gmsh verbosity level (0-5, higher = more verbose)
• gui - Whether to launch the Gmsh GUI after mesh generation

In [2]:

filename = "monopole.msh"
wavelength = 4.0
base_width = None
base_length = None
arm_length = None
arm_radius = None
gap_size = None
outer_boundary_radius = None
verbose = 5
gui = True

# Set default values
if arm_length is None:
    arm_length = wavelength / 4
if arm_radius is None:
    arm_radius = arm_length / 20
if gap_size is None:
    gap_size = arm_length / 100
if outer_boundary_radius is None:
    outer_boundary_radius = 1.5 * wavelength
if base_width is None:
    base_width = arm_radius * 4
if base_length is None:
    base_length = arm_radius * 4

filename = "monopole.msh" wavelength = 4.0 base_width = None base_length = None arm_length = None arm_radius = None gap_size = None outer_boundary_radius = None verbose = 5 gui = True # Set default values if arm_length is None: arm_length = wavelength / 4 if arm_radius is None: arm_radius = arm_length / 20 if gap_size is None: gap_size = arm_length / 100 if outer_boundary_radius is None: outer_boundary_radius = 1.5 * wavelength if base_width is None: base_width = arm_radius * 4 if base_length is None: base_length = arm_radius * 4

Initialize gmsh

In [3]:

gmsh.initialize()
kernel = gmsh.model.occ
gmsh.option.setNumber("General.Verbosity", verbose)

# Create a new model. The name dipole is not important. If a model was already added,
# remove it first (this is useful when interactively evaluating this function).
if "monopole" in gmsh.model.list():
    gmsh.model.setCurrent("monopole")
    gmsh.model.remove()
gmsh.model.add("monopole")

gmsh.initialize() kernel = gmsh.model.occ gmsh.option.setNumber("General.Verbosity", verbose) # Create a new model. The name dipole is not important. If a model was already added, # remove it first (this is useful when interactively evaluating this function). if "monopole" in gmsh.model.list(): gmsh.model.setCurrent("monopole") gmsh.model.remove() gmsh.model.add("monopole")

In [4]:

# addSphere: The first three parameters are the coordinates of the center, and the last one is the radius.
outer_boundary = kernel.addSphere(0, 0, 0, outer_boundary_radius)

# addCylinder: The first three parameters are the coordinates of the center of the cylinder base,
# the second three defines its axis and the last one its radius.
arm = kernel.addCylinder(0, 0, gap_size / 2, 0, 0, arm_length, arm_radius)

# addRectangle: The first three parameters are the coordinates of the left corner of the rectangle, 
# and the next two define the width and length of the rectangle.
base = kernel.addRectangle(-base_width/2, -base_length/2, -gap_size/2,
                            base_width, base_length)


# Create gap rectangle (port region) and rotate to XZ plane (we need to do this because
# OpenCASCADE does not have a primitive to create a rectangle directly on the XZ
# plane...).
gap_rectangle = kernel.addRectangle(-arm_radius, -gap_size/2, 0, 2*arm_radius, gap_size)
kernel.rotate([(2, gap_rectangle)], 0, 0, 0, 1, 0, 0, math.pi/2)

kernel.synchronize()

# addSphere: The first three parameters are the coordinates of the center, and the last one is the radius. outer_boundary = kernel.addSphere(0, 0, 0, outer_boundary_radius) # addCylinder: The first three parameters are the coordinates of the center of the cylinder base, # the second three defines its axis and the last one its radius. arm = kernel.addCylinder(0, 0, gap_size / 2, 0, 0, arm_length, arm_radius) # addRectangle: The first three parameters are the coordinates of the left corner of the rectangle, # and the next two define the width and length of the rectangle. base = kernel.addRectangle(-base_width/2, -base_length/2, -gap_size/2, base_width, base_length) # Create gap rectangle (port region) and rotate to XZ plane (we need to do this because # OpenCASCADE does not have a primitive to create a rectangle directly on the XZ # plane...). gap_rectangle = kernel.addRectangle(-arm_radius, -gap_size/2, 0, 2*arm_radius, gap_size) kernel.rotate([(2, gap_rectangle)], 0, 0, 0, 1, 0, 0, math.pi/2) kernel.synchronize()

In [5]:

# Define the entities which later will generate the physical groups.
entities = [
    Entity("arm",            dim=3, mesh_order=1, tags=[arm]),
    Entity("outer_boundary", dim=3, mesh_order=2, tags=[outer_boundary]),
    Entity("base",           dim=2, mesh_order=1, tags=[base]),
    Entity("port",           dim=2, mesh_order=0, tags=[gap_rectangle]),
]

# Boolean operations to guarantee a nice mesh, algo it returns the
# physical group map.
pg_map = run_meshing_pipeline(entities)

print(entities)

# Refine near the port
refine_near_surfaces(entities[-1].dimtags, 
                     wavelength, 
                     ppw_near=10, 
                     ppw_far=10, 
                     set_as_background=True,
                     local_refinements = {entities[0].dimtags[0]: 10})


############# If the mesh is finer the kernel dies, the problem is duplicate meshes ##################

# Mesh sizes
mesh_sizes = {}

generate_3d_mesh(entities, mesh_sizes, filename, optimize=False)


# Mesh visualization, rendering transparent the outer boundary.
view_mesh(filename, transparent_groups= "outer_boundary__None")

# Define the entities which later will generate the physical groups. entities = [ Entity("arm", dim=3, mesh_order=1, tags=[arm]), Entity("outer_boundary", dim=3, mesh_order=2, tags=[outer_boundary]), Entity("base", dim=2, mesh_order=1, tags=[base]), Entity("port", dim=2, mesh_order=0, tags=[gap_rectangle]), ] # Boolean operations to guarantee a nice mesh, algo it returns the # physical group map. pg_map = run_meshing_pipeline(entities) print(entities) # Refine near the port refine_near_surfaces(entities[-1].dimtags, wavelength, ppw_near=10, ppw_far=10, set_as_background=True, local_refinements = {entities[0].dimtags[0]: 10}) ############# If the mesh is finer the kernel dies, the problem is duplicate meshes ################## # Mesh sizes mesh_sizes = {} generate_3d_mesh(entities, mesh_sizes, filename, optimize=False) # Mesh visualization, rendering transparent the outer boundary. view_mesh(filename, transparent_groups= "outer_boundary__None")

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Info    : [ 80%] Difference - Splitting faces                                                                                
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Info    : [ 80%] Difference - Making faces                                                                                
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  Physical group 'arm' (dim=3): pg=1, tags=[2]
  Physical group 'outer_boundary' (dim=3): pg=2, tags=[1]
  Physical group 'base' (dim=2): pg=3, tags=[5]
  Physical group 'port' (dim=2): pg=4, tags=[6]
  Physical group 'arm__outer_boundary' (dim=2): pg=5, tags=[7, 3, 8, 9]
  Physical group 'outer_boundary__None' (dim=2): pg=6, tags=[10]
[Entity('arm', dim=3, order=1, tags=[2]), Entity('outer_boundary', dim=3, order=2, tags=[1]), Entity('base', dim=2, order=1, tags=[5]), Entity('port', dim=2, order=0, tags=[6])]
  ppw_near=10  ppw_far=10
  SizeMax=0.4000  transition=1.0000
  global: 4 curves, SizeMin=0.4000
  local (3, 2): 4 curves, SizeMin=0.4000
  Merged 2 fields with Min → field 5
Info    : Meshing 1D...
Info    : [  0%] Meshing curve 4 (Circle)
Info    : [ 10%] Meshing curve 11 (Line)
Info    : [ 20%] Meshing curve 18 (Line)
Info    : [ 30%] Meshing curve 19 (Line)
Info    : [ 30%] Meshing curve 20 (Line)
Info    : [ 40%] Meshing curve 21 (Line)
Info    : [ 50%] Meshing curve 22 (Line)
Info    : [ 50%] Meshing curve 23 (Circle)
Info    : [ 60%] Meshing curve 24 (Circle)
Info    : [ 70%] Meshing curve 25 (Line)
Info    : [ 80%] Meshing curve 27 (Circle)
Info    : [ 90%] Meshing curve 29 (Line)
Info    : [100%] Meshing curve 30 (Line)
Info    : Done meshing 1D (Wall 0.000626497s, CPU 0.001006s)
Info    : Meshing 2D...
Info    : [  0%] Meshing surface 3 (Plane, MeshAdapt)
Info    : [ 20%] Meshing surface 5 (Plane, MeshAdapt)
Info    : [ 30%] Meshing surface 6 (Plane, MeshAdapt)
Info    : [ 50%] Meshing surface 7 (Cylinder, MeshAdapt)
Info    : [ 60%] Meshing surface 8 (Plane, MeshAdapt)
Info    : [ 80%] Meshing surface 9 (Plane, MeshAdapt)
Info    : [ 90%] Meshing surface 10 (Sphere, MeshAdapt)

Warning : Unknown curve 3
Warning : Unknown curve 7
Warning : Unknown curve 8
Warning : Unknown curve 9

Info    : Done meshing 2D (Wall 1.39879s, CPU 1.39058s)
Info    : Meshing 3D...
Info    : 3D Meshing 2 volumes with 1 connected component
Info    : Tetrahedrizing 3787 nodes...
Info    : Done tetrahedrizing 3795 nodes (Wall 0.0159201s, CPU 0.013948s)
Info    : Reconstructing mesh...
Info    :  - Creating surface mesh
Info    :  - Identifying boundary edges
Info    :  - Recovering boundary
Info    : Done reconstructing mesh (Wall 0.0569669s, CPU 0.052378s)
Info    : Found void region
Info    : Found void region
Info    : Found volume 1
Info    : It. 0 - 0 nodes created - worst tet radius 19.0604 (nodes removed 0 0)

Info    : It. 500 - 290 nodes created - worst tet radius 2.81913 (nodes removed 196 14)
Info    : It. 1000 - 604 nodes created - worst tet radius 4.04623 (nodes removed 378 18)
Info    : It. 1500 - 915 nodes created - worst tet radius 3.21896 (nodes removed 560 25)
Info    : It. 2000 - 1260 nodes created - worst tet radius 1.81445 (nodes removed 711 29)
Info    : It. 2500 - 1649 nodes created - worst tet radius 1.67168 (nodes removed 822 29)
Info    : It. 3000 - 1967 nodes created - worst tet radius 1.58062 (nodes removed 1002 31)

Info    : It. 3500 - 2322 nodes created - worst tet radius 1.50431 (nodes removed 1147 31)
Info    : It. 4000 - 2753 nodes created - worst tet radius 1.42108 (nodes removed 1216 31)
Info    : It. 4500 - 3116 nodes created - worst tet radius 1.36812 (nodes removed 1350 34)
Info    : It. 5000 - 3565 nodes created - worst tet radius 1.31129 (nodes removed 1401 34)
Info    : It. 5500 - 3982 nodes created - worst tet radius 1.26759 (nodes removed 1484 34)
Info    : It. 6000 - 4401 nodes created - worst tet radius 1.2293 (nodes removed 1565 34)

Info    : It. 6500 - 4785 nodes created - worst tet radius 1.1961 (nodes removed 1681 34)
Info    : It. 7000 - 5224 nodes created - worst tet radius 1.16455 (nodes removed 1742 34)
Info    : It. 7500 - 5595 nodes created - worst tet radius 1.14187 (nodes removed 1871 34)
Info    : It. 8000 - 5958 nodes created - worst tet radius 1.11892 (nodes removed 2006 36)
Info    : It. 8500 - 6347 nodes created - worst tet radius 2.13568 (nodes removed 2117 36)

Info    : It. 9000 - 6725 nodes created - worst tet radius 2.74428 (nodes removed 2237 38)
Info    : It. 9500 - 7142 nodes created - worst tet radius 1.05564 (nodes removed 2320 38)
Info    : It. 10000 - 7568 nodes created - worst tet radius 1.03647 (nodes removed 2393 39)
Info    : It. 10500 - 7996 nodes created - worst tet radius 1.0195 (nodes removed 2464 40)
Info    : It. 11000 - 8405 nodes created - worst tet radius 1.00275 (nodes removed 2553 42)
Info    : 3D refinement terminated (12263 nodes total):
Info    :  - 12 Delaunay cavities modified for star shapeness
Info    :  - 2595 nodes could not be inserted
Info    :  - 65658 tetrahedra created in 1.06612 sec. (61585 tets/s)
Info    : 236 node relocations

Warning : No elements in volume 2

Info    : Done meshing 3D (Wall 1.23683s, CPU 1.23211s)
Info    : Optimizing mesh...
Info    : Optimizing volume 1
Info    : Optimization starts (volume = 903.36) with worst = 7.35983e-05 / average = 0.77033:
Info    : 0.00 < quality < 0.10 :       240 elements
Info    : 0.10 < quality < 0.20 :       493 elements
Info    : 0.20 < quality < 0.30 :       804 elements
Info    : 0.30 < quality < 0.40 :      1272 elements
Info    : 0.40 < quality < 0.50 :      1962 elements
Info    : 0.50 < quality < 0.60 :      3306 elements
Info    : 0.60 < quality < 0.70 :      7285 elements
Info    : 0.70 < quality < 0.80 :     15064 elements
Info    : 0.80 < quality < 0.90 :     23592 elements
Info    : 0.90 < quality < 1.00 :     11640 elements
Info    : 1355 edge swaps, 121 node relocations (volume = 903.36): worst = 0.0011262 / average = 0.782825 (Wall 0.0442572s, CPU 0.04392s)
Info    : 1426 edge swaps, 158 node relocations (volume = 903.36): worst = 0.00152376 / average = 0.783046 (Wall 0.0548058s, CPU 0.053618s)
Info    : 1452 edge swaps, 198 node relocations (volume = 903.36): worst = 0.00152539 / average = 0.783157 (Wall 0.0656043s, CPU 0.064399s)

Info    : 1462 edge swaps, 220 node relocations (volume = 903.36): worst = 0.00152541 / average = 0.783174 (Wall 0.0759062s, CPU 0.075295s)
Info    : No ill-shaped tets in the mesh :-)
Info    : 0.00 < quality < 0.10 :        38 elements
Info    : 0.10 < quality < 0.20 :        47 elements
Info    : 0.20 < quality < 0.30 :        72 elements
Info    : 0.30 < quality < 0.40 :      1301 elements
Info    : 0.40 < quality < 0.50 :      1889 elements
Info    : 0.50 < quality < 0.60 :      3231 elements
Info    : 0.60 < quality < 0.70 :      7216 elements
Info    : 0.70 < quality < 0.80 :     15272 elements
Info    : 0.80 < quality < 0.90 :     23778 elements
Info    : 0.90 < quality < 1.00 :     11603 elements
Info    : Optimizing volume 2
Info    : Done optimizing mesh (Wall 0.216602s, CPU 0.211705s)
Info    : 12263 nodes 72116 elements
Info    : Writing 'monopole.msh'...
Mesh saved to monopole.msh
Info    : Done writing 'monopole.msh'
  Nodes: 12263
  Elements: 72116

Warning : ------------------------------
Warning : Mesh generation error summary
Warning :     5 warnings
Warning :     0 errors
Warning : Check the full log for details
Warning : ------------------------------

Loading mesh file: monopole.msh
Groups to render transparent: outer_boundary__None

Mesh loaded successfully with 2 cell blocks
Found 7563 triangles total
Physical group tags in mesh: {3: 'base', 4: 'port', 5: 'arm__outer_boundary', 6: 'outer_boundary__None'}