Coaxial cable mesh¶

In [1]:

from palacetoolkit.viz import run_with_scrollable_output, view_mesh
from palacetoolkit.geometry import extract_tag, xmin, xmax, ymin, ymax, zmin, zmax
import math
import gmsh

from palacetoolkit.viz import run_with_scrollable_output, view_mesh from palacetoolkit.geometry import extract_tag, xmin, xmax, ymin, ymax, zmin, zmax import math import gmsh

Parameters:

• filename - the filename to use for the generated mesh.
• refinement - measure of how many elements to include, 0 is least
• order - the polynomial order of the approximation, minimum 1
• inner_diameter_mm - the inner diameter of the cable, in millimeters
• outer_diameter_mm - the outer diameter of the cable, in millimeters
• length_mm - the length of the cable, in millimeters
• verbose - flag to dictate the level of print to REPL, passed to Gmsh
• gui - whether to launch the Gmsh GUI on mesh generation

In [2]:

filename : str = "coax.msh" 
refinement : int = 2 
order : int = 2 
inner_diameter_mm : float = 1.6383 
outer_diameter_mm : float = 5.461 
length_mm : float = 40.0
verbose : int = 5
gui : bool = True 

filename : str = "coax.msh" refinement : int = 2 order : int = 2 inner_diameter_mm : float = 1.6383 outer_diameter_mm : float = 5.461 length_mm : float = 40.0 verbose : int = 5 gui : bool = True

Check that the geometry makes sense.

In [3]:

assert outer_diameter_mm > inner_diameter_mm > 0
assert length_mm > 0
assert refinement >= 0
assert order > 0     

assert outer_diameter_mm > inner_diameter_mm > 0 assert length_mm > 0 assert refinement >= 0 assert order > 0

Initialization of the model.¶

In [4]:

# Creates a reference to the geometry module based on OpenCASCADE (OCC).
kernel = gmsh.model.occ

# Initialize gmsh.
gmsh.initialize()

# Set the verbosity of the output.
gmsh.option.setNumber("General.Verbosity", verbose)

# Creates a reference to the geometry module based on OpenCASCADE (OCC). kernel = gmsh.model.occ # Initialize gmsh. gmsh.initialize() # Set the verbosity of the output. gmsh.option.setNumber("General.Verbosity", verbose)

Geometry definitions.¶

In [5]:

# Geometry (en mm)
inner_radio = inner_diameter_mm / 2
outer_radio = outer_diameter_mm / 2

# Mesh parameters
n_circum = 4 * 2**refinement 
n_length = 4 * 2**refinement
    
# Geometry
p0 = kernel.addPoint(inner_radio, 0, 0)
p1 = kernel.addPoint(outer_radio, 0, 0)

l0 = kernel.addLine(p0, p1)

# Geometry (en mm) inner_radio = inner_diameter_mm / 2 outer_radio = outer_diameter_mm / 2 # Mesh parameters n_circum = 4 * 2**refinement n_length = 4 * 2**refinement # Geometry p0 = kernel.addPoint(inner_radio, 0, 0) p1 = kernel.addPoint(outer_radio, 0, 0) l0 = kernel.addLine(p0, p1)

Revolve operation - base face generation.¶

Rotate the line (l_0) around the z-axis.

• First revolve (base_face_0) is made with a 180° degree and n_circum//2 divisions.
• Seconde revolve (base_face_1) with a -180° degree and n_circum//2 divisions.

In [6]:

base_face_0 = kernel.revolve(
        [(1, l0)],          # list of entities to rotate (dim=1 → curve, tag=l0)
        0.0, 0.0, 0.0,      # origin point of rotation
        0.0, 0.0, 1.0,      # rotation axis (here, the z-axis)
        math.pi,            # rotation angle (180°)
        [n_circum // 2],    # number of divisions in the angular direction
        [1.0],              # scale factor for the mesh size (1.0 means no scaling)
        recombine=True      # recombinar las caras resultantes
        )
    
base_face_1 = kernel.revolve(
    [(1, l0)],         
    0.0, 0.0, 0.0,      
    0.0, 0.0, 1.0,      
    -math.pi,        
    [n_circum//2],         
    [1.0],             
    recombine=True     
)

base_face_0 = kernel.revolve( [(1, l0)], # list of entities to rotate (dim=1 → curve, tag=l0) 0.0, 0.0, 0.0, # origin point of rotation 0.0, 0.0, 1.0, # rotation axis (here, the z-axis) math.pi, # rotation angle (180°) [n_circum // 2], # number of divisions in the angular direction [1.0], # scale factor for the mesh size (1.0 means no scaling) recombine=True # recombinar las caras resultantes ) base_face_1 = kernel.revolve( [(1, l0)], 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -math.pi, [n_circum//2], [1.0], recombine=True )

kernel.revolve returns a list of entities created by the revolution, each one represented as a tuple (dim, tag).

• dim is the dimension of the entity (0 for points, 1 for lines, 2 for surfaces, 3 for volumes).
• A tag is a unique identifier assigned by Gmsh to each entity created.

We will filter these lists to keep only the surfaces (dim=2) that represent the cylinder faces, discarding any other entities that may have been created during the revolution.

In this case the revolution returns [(1, 4), (2, 1), (1, 2), (1, 3)]. We are only interested in (2, 1), which is the surface created by the revolution, and we discard the lines (1, 4), (1, 2), (1, 3).

In [7]:

base_face_0 = [x for x in base_face_0 if x[0] == 2]
base_face_1 = [x for x in base_face_1 if x[0] == 2]

# Check that there was generated only one face.
assert len(base_face_0) == 1 and len(base_face_1) == 1

base_face_0 = [x for x in base_face_0 if x[0] == 2] base_face_1 = [x for x in base_face_1 if x[0] == 2] # Check that there was generated only one face. assert len(base_face_0) == 1 and len(base_face_1) == 1

Now, we extrude the base faces to get the cylinder.

In [8]:

# Extrude the faces along the z-axis. 
cylinder_0 = kernel.extrude(
    base_face_0,          # List of entities (dim=2, tag)
    0.0, 0.0, length_mm,  # How much extrusion in (x, y, z)
    [n_length],           # Divisions in the direction of the extrusion
    [1.0],                # Scale
    recombine=True        # recombine faces
)

cylinder_1 = kernel.extrude(
    base_face_1,
    0.0, 0.0, length_mm,
    [n_length],
    [1.0],
    recombine=True
)

# Extrude the faces along the z-axis. cylinder_0 = kernel.extrude( base_face_0, # List of entities (dim=2, tag) 0.0, 0.0, length_mm, # How much extrusion in (x, y, z) [n_length], # Divisions in the direction of the extrusion [1.0], # Scale recombine=True # recombine faces ) cylinder_1 = kernel.extrude( base_face_1, 0.0, 0.0, length_mm, [n_length], [1.0], recombine=True )

We keep only the tags of the faces and volumes created by the extrusion, filtering by dimension. Remember that cylinder_0 and cylinder_1 are lists of tuples (dim, tag) representing all entities created by the extrusion, including lines, surfaces, and volumes. We are interested only in the faces (dim=2) that form the cylinder end caps, and in the volumes (dim=3) that represent the cylinder body.

In [9]:

base_face_0 = base_face_0[0][1]   # Tag of the first surface.
base_face_1 = base_face_1[0][1]   

far_face_0 = cylinder_0[0][1] 
cylinder_0 = cylinder_0[1][1] 

far_face_1 = cylinder_1[0][1]
cylinder_1 = cylinder_1[1][1]

base_face_0 = base_face_0[0][1] # Tag of the first surface. base_face_1 = base_face_1[0][1] far_face_0 = cylinder_0[0][1] cylinder_0 = cylinder_0[1][1] far_face_1 = cylinder_1[0][1] cylinder_1 = cylinder_1[1][1]

Fragment the geometry to create a valid mesh. This is necessary because we have extruded two faces that share an edge, and we need to ensure that the resulting geometry is properly connected.

In [10]:

# Remove duplicates (if there is any) and preserve the original geometry.
kernel.fragment(kernel.getEntities(), [])
kernel.synchronize()

# Remove duplicates (if there is any) and preserve the original geometry. kernel.fragment(kernel.getEntities(), []) kernel.synchronize()

Info    : [  0%] Fragments                                                                                  
Info    : [ 10%] Fragments                                                                                  
Info    : [ 20%] Fragments                                                                                  
Info    : [ 30%] Fragments                                                                                  
Info    : [ 40%] Fragments                                                                                  
Info    : [ 50%] Fragments                                                                                  
Info    : [ 60%] Fragments                                                                                  
Info    : [ 70%] Fragments - Filling splits of vertices                                                                                
Info    : [ 80%] Fragments - Splitting faces                                                                                
Info    : [ 90%] Fragments - Looking for internal shapes                                                                                
                                                                                
Info    : Rebinding OpenCASCADE point 3
Info    : Rebinding OpenCASCADE point 4
Info    : Cannot bind existing OpenCASCADE point 3 to second tag 5
Info    : Could not preserve tag of 0D object 5 (->3)
Info    : Cannot bind existing OpenCASCADE point 4 to second tag 6
Info    : Could not preserve tag of 0D object 6 (->4)
Info    : Rebinding OpenCASCADE point 7
Info    : Rebinding OpenCASCADE point 8
Info    : Rebinding OpenCASCADE point 9
Info    : Rebinding OpenCASCADE point 10
Info    : Cannot bind existing OpenCASCADE point 7 to second tag 11
Info    : Could not preserve tag of 0D object 11 (->7)
Info    : Cannot bind existing OpenCASCADE point 8 to second tag 12
Info    : Could not preserve tag of 0D object 12 (->8)
Info    : Cannot bind existing OpenCASCADE point 9 to second tag 13
Info    : Could not preserve tag of 0D object 13 (->9)
Info    : Cannot bind existing OpenCASCADE point 10 to second tag 14
Info    : Could not preserve tag of 0D object 14 (->10)
Info    : Rebinding OpenCASCADE curve 2
Info    : Rebinding OpenCASCADE curve 3
Info    : Rebinding OpenCASCADE curve 4
Info    : Rebinding OpenCASCADE curve 5
Info    : Rebinding OpenCASCADE curve 6
Info    : Cannot bind existing OpenCASCADE curve 4 to second tag 7
Info    : Could not preserve tag of 1D object 7 (->4)
Info    : Rebinding OpenCASCADE curve 8
Info    : Rebinding OpenCASCADE curve 9
Info    : Rebinding OpenCASCADE curve 10
Info    : Rebinding OpenCASCADE curve 11
Info    : Rebinding OpenCASCADE curve 12
Info    : Rebinding OpenCASCADE curve 13
Info    : Rebinding OpenCASCADE curve 14
Info    : Rebinding OpenCASCADE curve 15
Info    : Cannot bind existing OpenCASCADE curve 8 to second tag 16
Info    : Could not preserve tag of 1D object 16 (->8)
Info    : Cannot bind existing OpenCASCADE curve 9 to second tag 17
Info    : Could not preserve tag of 1D object 17 (->9)
Info    : Rebinding OpenCASCADE curve 18
Info    : Cannot bind existing OpenCASCADE curve 11 to second tag 19
Info    : Could not preserve tag of 1D object 19 (->11)
Info    : Cannot bind existing OpenCASCADE curve 12 to second tag 20
Info    : Could not preserve tag of 1D object 20 (->12)
Info    : Rebinding OpenCASCADE curve 21
Info    : Cannot bind existing OpenCASCADE curve 14 to second tag 22
Info    : Could not preserve tag of 1D object 22 (->14)
Info    : Cannot bind existing OpenCASCADE curve 15 to second tag 23
Info    : Could not preserve tag of 1D object 23 (->15)
Info    : Rebinding OpenCASCADE surface 1
Info    : Rebinding OpenCASCADE surface 2
Info    : Rebinding OpenCASCADE surface 3
Info    : Rebinding OpenCASCADE surface 4
Info    : Rebinding OpenCASCADE surface 5
Info    : Rebinding OpenCASCADE surface 6
Info    : Rebinding OpenCASCADE surface 7
Info    : Rebinding OpenCASCADE surface 8
Info    : Rebinding OpenCASCADE surface 9
Info    : Cannot bind existing OpenCASCADE surface 5 to second tag 10
Info    : Could not preserve tag of 2D object 10 (->5)
Info    : Cannot bind existing OpenCASCADE surface 6 to second tag 11
Info    : Could not preserve tag of 2D object 11 (->6)
Info    : Rebinding OpenCASCADE surface 12

In [11]:

# Get the boundaries deleting non necessary surfaces
boundaries = []
for cylinder in [cylinder_0, cylinder_1]:
    _, local_boundaries = gmsh.model.getAdjacencies(3, cylinder)
    local_delete = []
    for boundary in local_boundaries:
        if boundary not in boundaries:
            boundaries.append(boundary)
        else:
            local_delete.append(boundaries.index(boundary))
    # eliminar duplicados
    for idx in sorted(local_delete, reverse=True):
        del boundaries[idx]

# Delete faces
for face in [base_face_0, base_face_1, far_face_0, far_face_1]:
    if face in boundaries:
        boundaries.remove(face)

# Get the boundaries deleting non necessary surfaces boundaries = [] for cylinder in [cylinder_0, cylinder_1]: _, local_boundaries = gmsh.model.getAdjacencies(3, cylinder) local_delete = [] for boundary in local_boundaries: if boundary not in boundaries: boundaries.append(boundary) else: local_delete.append(boundaries.index(boundary)) # eliminar duplicados for idx in sorted(local_delete, reverse=True): del boundaries[idx] # Delete faces for face in [base_face_0, base_face_1, far_face_0, far_face_1]: if face in boundaries: boundaries.remove(face)

Defining the Physical groups.¶

In [12]:

cylinder_group = gmsh.model.addPhysicalGroup(3, [cylinder_0, cylinder_1], -1, "cylinder") 
boundary_group = gmsh.model.addPhysicalGroup(2, boundaries, -1, "boundaries") 
port1_group = gmsh.model.addPhysicalGroup(2, [base_face_0, base_face_1], -1, "port1") 
port2_group = gmsh.model.addPhysicalGroup(2, [far_face_0, far_face_1], -1, "port2")

cylinder_group = gmsh.model.addPhysicalGroup(3, [cylinder_0, cylinder_1], -1, "cylinder") boundary_group = gmsh.model.addPhysicalGroup(2, boundaries, -1, "boundaries") port1_group = gmsh.model.addPhysicalGroup(2, [base_face_0, base_face_1], -1, "port1") port2_group = gmsh.model.addPhysicalGroup(2, [far_face_0, far_face_1], -1, "port2")

Mesh settings and generation.¶

In [13]:

def _generate_coax_mesh():
    # Mesh options
    gmsh.option.setNumber("Mesh.MinimumCurveNodes", 2)
    gmsh.option.setNumber("Mesh.MinimumCircleNodes", 0)
    gmsh.option.setNumber("Mesh.MeshSizeFromPoints", 0)
    gmsh.option.setNumber("Mesh.MeshSizeFromCurvature", 0)
    gmsh.option.setNumber("Mesh.MeshSizeExtendFromBoundary", 0)

    # Set mesh algorithms
    gmsh.option.setNumber("Mesh.Algorithm", 6)   # frontal (2D)
    gmsh.option.setNumber("Mesh.Algorithm3D", 1) # Delaunay (3D)

    # Generate 3D mesh
    gmsh.model.mesh.generate(3)

    # Order of the mesh elements (1 = linear, 2 = quadratic)
    gmsh.model.mesh.setOrder(order)

    # Save mesh
    gmsh.option.setNumber("Mesh.MshFileVersion", 2.2)
    gmsh.option.setNumber("Mesh.Binary", 1)
    gmsh.write(filename)

    if verbose > 0:
        print("\nFinished generating mesh. Physical group tags:")
        print("Cylinder:", cylinder_group)
        print("Boundaries:", boundary_group)
        print("Port 1:", port1_group)
        print("Port 2:", port2_group)
        print()

run_with_scrollable_output(_generate_coax_mesh, title="Coax mesh generation", max_lines=10)

if gui:
    gmsh.fltk.run()

gmsh.finalize()
view_mesh(filename)

def _generate_coax_mesh(): # Mesh options gmsh.option.setNumber("Mesh.MinimumCurveNodes", 2) gmsh.option.setNumber("Mesh.MinimumCircleNodes", 0) gmsh.option.setNumber("Mesh.MeshSizeFromPoints", 0) gmsh.option.setNumber("Mesh.MeshSizeFromCurvature", 0) gmsh.option.setNumber("Mesh.MeshSizeExtendFromBoundary", 0) # Set mesh algorithms gmsh.option.setNumber("Mesh.Algorithm", 6) # frontal (2D) gmsh.option.setNumber("Mesh.Algorithm3D", 1) # Delaunay (3D) # Generate 3D mesh gmsh.model.mesh.generate(3) # Order of the mesh elements (1 = linear, 2 = quadratic) gmsh.model.mesh.setOrder(order) # Save mesh gmsh.option.setNumber("Mesh.MshFileVersion", 2.2) gmsh.option.setNumber("Mesh.Binary", 1) gmsh.write(filename) if verbose > 0: print("\nFinished generating mesh. Physical group tags:") print("Cylinder:", cylinder_group) print("Boundaries:", boundary_group) print("Port 1:", port1_group) print("Port 2:", port2_group) print() run_with_scrollable_output(_generate_coax_mesh, title="Coax mesh generation", max_lines=10) if gui: gmsh.fltk.run() gmsh.finalize() view_mesh(filename)

Finished generating mesh. Physical group tags:
Cylinder: 1
Boundaries: 2
Port 1: 3
Port 2: 4

-------------------------------------------------------
Version       : 4.15.2
License       : GNU General Public License
Build OS      : Linux64-sdk
Build date    : 20260324
Build host    : gmsh.info
Build options : 64Bit ALGLIB[contrib] ANN[contrib] Bamg Blas[petsc] Blossom Cgns DIntegration Dlopen DomHex Eigen[contrib] Fltk Gmm[contrib] Hxt Jpeg Kbipack Lapack[petsc] LinuxJoystick MathEx[contrib] Med Mesh Metis[contrib] Mmg Mpeg Netgen Nii2mesh ONELAB ONELABMetamodel OpenCASCADE OpenCASCADE-CAF OpenGL OpenMP OptHom PETSc Parser Plugins Png Post QuadMeshingTools QuadTri Solver TetGen/BR TinyXML2[contrib] Untangle Voro++[contrib] WinslowUntangler Zlib tinyobjloader
FLTK version  : 1.3.11
PETSc version : 3.14.4 (real arithmtic)
OCC version   : 7.8.1
MED version   : 4.1.0
Packaged by   : geuzaine
Web site      : https://gmsh.info
Issue tracker : https://gitlab.onelab.info/gmsh/gmsh/issues
-------------------------------------------------------

Loading mesh file: coax.msh
Groups to render transparent: ['air_none', 'air_plastic_enclosure']

Mesh loaded successfully with 2 cell blocks
Found 1088 triangles total
Physical group tags in mesh: {2: 'boundaries', 3: 'port1', 4: 'port2'}