From 424f6eee9bbc8a2ba699e723fd322072c6b7235e Mon Sep 17 00:00:00 2001
From: Emily Boudreaux <thomas@boudreauxmail.com>
Date: Wed, 30 Apr 2025 07:26:58 -0400
Subject: [PATCH] refactor(meshGeneration): working on gmsh to generate
 curvilinear isogeomatric spherical mesh

---
 utils/meshGeneration/genSphere_tmp.msh   |  6966 ++++++
 utils/meshGeneration/generateMFEMMesh.py |    73 +
 utils/meshGeneration/generateMesh.py     |    56 +-
 utils/meshGeneration/readme.md           |     2 +-
 utils/meshGeneration/sphere.geo          |    38 +
 utils/meshGeneration/sphere.mesh         |   261 +
 utils/meshGeneration/sphere.msh          | 24497 +++++++++++++++++++++
 utils/meshGeneration/sphere.vtk          |  7979 +++++++
 utils/meshGeneration/sphere.vtu          |   Bin 0 -> 316952 bytes
 utils/meshGeneration/sphere_order2.msh   |  1503 ++
 utils/meshGeneration/sphere_order2.vtk   |  2317 ++
 11 files changed, 43664 insertions(+), 28 deletions(-)
 create mode 100644 utils/meshGeneration/genSphere_tmp.msh
 create mode 100644 utils/meshGeneration/sphere.geo
 create mode 100644 utils/meshGeneration/sphere.mesh
 create mode 100644 utils/meshGeneration/sphere.msh
 create mode 100644 utils/meshGeneration/sphere.vtk
 create mode 100644 utils/meshGeneration/sphere.vtu
 create mode 100644 utils/meshGeneration/sphere_order2.msh
 create mode 100644 utils/meshGeneration/sphere_order2.vtk

diff --git a/utils/meshGeneration/genSphere_tmp.msh b/utils/meshGeneration/genSphere_tmp.msh
new file mode 100644
index 0000000..7785fd9
--- /dev/null
+++ b/utils/meshGeneration/genSphere_tmp.msh
@@ -0,0 +1,6966 @@
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+$EndElements
diff --git a/utils/meshGeneration/generateMFEMMesh.py b/utils/meshGeneration/generateMFEMMesh.py
index e69de29..2b0300c 100644
--- a/utils/meshGeneration/generateMFEMMesh.py
+++ b/utils/meshGeneration/generateMFEMMesh.py
@@ -0,0 +1,73 @@
+import math
+from icosphere import icosphere
+
+def generate_mfem_sphere_mesh(subdivisions: int, outputFile: str):
+    """Generate a P2 triangular sphere mesh and save in MFEM mesh v1.x format."""
+    # 1. Generate a geodesic icosphere
+    vertices, faces = icosphere(subdivisions)  # returns (Nverts×3) array and list of 3-tuples :contentReference[oaicite:14]{index=14}
+
+    # 2. Build unique edges and mid-edge nodes
+    edgeToMidIndex = {}
+    edgesSet = set()
+    for tri in faces:
+        for i in range(3):
+            v0, v1 = tri[i], tri[(i+1) % 3]
+            edge = tuple(sorted((v0, v1)))
+            edgesSet.add(edge)
+
+    midPoints = []
+    for edge in edgesSet:
+        v0, v1 = edge
+        x0, y0, z0 = vertices[v0]
+        x1, y1, z1 = vertices[v1]
+        mx, my, mz = (x0 + x1)/2, (y0 + y1)/2, (z0 + z1)/2
+        r = math.sqrt(mx*mx + my*my + mz*mz)
+        mx, my, mz = mx/r, my/r, mz/r  # project onto unit sphere :contentReference[oaicite:15]{index=15}
+        edgeToMidIndex[edge] = len(vertices) + len(midPoints)
+        midPoints.append((mx, my, mz))
+
+    # 3. Assemble all node coordinates (vertices + mid-edge nodes)
+    nodeCoords = [tuple(v) for v in vertices] + midPoints
+
+    # 4. Write MFEM mesh file
+    with open(outputFile, 'w') as f:
+        # Header
+        f.write("MFEM mesh v1.0\n\n")
+
+        # Topology
+        f.write("dimension\n2\n\n")
+        f.write(f"elements\n{len(faces)}\n")
+        for tri in faces:
+            v0, v1, v2 = tri
+            m0 = edgeToMidIndex[tuple(sorted((v0, v1)))]
+            m1 = edgeToMidIndex[tuple(sorted((v1, v2)))]
+            m2 = edgeToMidIndex[tuple(sorted((v2, v0)))]
+            # attribute=1, type=2 (triangle), followed by 6 vertex indices for P2 :contentReference[oaicite:16]{index=16}
+            f.write(f"1 2 {v0} {v1} {v2} {m0} {m1} {m2}\n")
+        f.write("\n")
+
+        # No boundary segments for a closed surface
+        f.write("boundary\n0\n\n")
+
+        # Vertices count (actual DOFs)
+        f.write(f"vertices\n{len(nodeCoords)}\n\n")
+
+        # Geometry: Nodes (P2 in 3D)
+        f.write("nodes\n")
+        f.write("FiniteElementSpace\n")
+        f.write("FiniteElementCollection: H1_3D_P2\n")
+        f.write("VDim: 3\n")
+        f.write("Ordering: 1\n")
+        for x, y, z in nodeCoords:
+            f.write(f"{x} {y} {z}\n")
+
+if __name__ == "__main__":
+    import argparse
+    parser = argparse.ArgumentParser(description='Generate a spherical mesh in MFEM format')
+    parser.add_argument('--subdivisions', type=int, default=2, help='Number of subdivisions for the icosphere')
+    parser.add_argument('--output', type=str, default='sphere.mesh', help='Output file name')
+    args = parser.parse_args()
+
+    # Generate the mesh
+    generate_mfem_sphere_mesh(args.subdivisions, args.output)
+    print(f"MFEM mesh generated: {args.output}")
\ No newline at end of file
diff --git a/utils/meshGeneration/generateMesh.py b/utils/meshGeneration/generateMesh.py
index b758f43..783b5da 100644
--- a/utils/meshGeneration/generateMesh.py
+++ b/utils/meshGeneration/generateMesh.py
@@ -1,37 +1,39 @@
-import pygmsh
 import meshio
-import numpy as np
-from math import sqrt
-
 import argparse
+import subprocess as sp
+import os
 
-def mesh_size_callback(dim, tag, x, y, z, lc, a, b, k):
-    r = np.sqrt(x**2 + y**2 + z**2)
-    size = a + (b-a) * (1-np.exp(-k*r))
-    return size
+def generateMesh(coreMeshRes, outerMeshRes, k, order):
+    # gmsh sphere.geo -3 -setnumber Parameters/Order 1 -setnumber Parameters/CoreRes 0.2 -setnumber Parameters/OuterRes 0.4 -setnumber Parameters/K 2.0 -o sphere_order2.msh
+    gmsh_cmd = [
+        'gmsh',
+        'sphere.geo',  # Path to your GMSH geometry file
+        '-3',  # Generate 3D mesh
+        '-setnumber', 'Parameters/Order', str(order),
+        '-setnumber', 'Parameters/CoreRes', str(coreMeshRes),
+        '-setnumber', 'Parameters/OuterRes', str(outerMeshRes),
+        '-setnumber', 'Parameters/K', str(k),
+        '-o', 'sphere.vtk',  # Output mesh file
+        '-format', 'vtk'
 
-def generate_spherical_mesh(radius=1.0, coreRes = 0.1, outRes = 0.1, k = 2):
-    with pygmsh.occ.Geometry() as geom:
-        originPoint = geom.add_point([0.0, 0.0, 0.0], mesh_size=coreRes)
-        geom.add_ball([0.0, 0.0, 0.0], 1.0)
-
-        geom.set_mesh_size_callback(lambda dim, tag, x, y, z, lc: mesh_size_callback(dim, tag, x, y, z, lc, coreRes, outRes, k))
-        mesh = geom.generate_mesh(verbose=True)
-
-    return mesh
-
-
-def write_mfem_mesh(meshData, filename):
-    meshio.write(filename, meshData, file_format='gmsh22')
+    ]
+    # Use popen to run
+    process = sp.Popen(gmsh_cmd)
+    stdout, stderr = process.communicate()
+    if process.returncode != 0:
+        print(f"Error generating mesh: {stderr.decode()}")
 
 if __name__ == '__main__':
     parser = argparse.ArgumentParser(description='Generate a spherical mesh')
-    parser.add_argument('--radius', type=float, default=1.0, help='Radius of the sphere')
-    parser.add_argument('--coreMeshRes', type=float, default=0.01, help='Core Mesh Resolution')
-    parser.add_argument('--outerMeshRes', type=float, default=0.1, help='Outer Mesh Resolution')
+    parser.add_argument('--coreMeshRes', type=float, default=0.1, help='Core Mesh Resolution target')
+    parser.add_argument('--outerMeshRes', type=float, default=0.3, help='Outer Mesh Resolution target')
     parser.add_argument('--k', type=float, default=2, help='Mesh size scaling factor')
-    parser.add_argument('--output', type=str, default='sphere.msh', help='Output file name')
+
+    # Add argument for element order
+    parser.add_argument('--order', type=int, default=2, help='Mesh element order (e.g., 1 for linear, 2 for quadratic)')
+    parser.add_argument('--output', type=str, default='sphere.vtk', help='Output file name')
     args = parser.parse_args()
 
-    meshData = generate_spherical_mesh(args.radius, args.coreMeshRes, args.outerMeshRes, args.k)
-    write_mfem_mesh(meshData, args.output)
+    # Generate the mesh
+    generateMesh(args.coreMeshRes, args.outerMeshRes, args.k, args.order)
+
diff --git a/utils/meshGeneration/readme.md b/utils/meshGeneration/readme.md
index 27c4d15..0e68ecb 100644
--- a/utils/meshGeneration/readme.md
+++ b/utils/meshGeneration/readme.md
@@ -5,4 +5,4 @@ This will produce a unit sphere mesh centered on (0, 0, 0) which can be rescaled
 
 ## Dependecies
 - pygmsh
-- meshio
\ No newline at end of file
+- meshio
diff --git a/utils/meshGeneration/sphere.geo b/utils/meshGeneration/sphere.geo
new file mode 100644
index 0000000..242a225
--- /dev/null
+++ b/utils/meshGeneration/sphere.geo
@@ -0,0 +1,38 @@
+SetFactory("OpenCASCADE");
+
+// Define parameters - these can be overridden from the command line
+// using the -setnumber flag, e.g., gmsh sphere.geo -setnumber Parameters/Order 2
+DefineConstant[
+  radius = {1.0, Name "Parameters/Radius"},
+  coreRes = {0.01, Name "Parameters/CoreRes"},
+  outerRes = {0.1, Name "Parameters/OuterRes"},
+  kVal = {2.0, Name "Parameters/K"},
+  order = {2, Name "Parameters/Order"} // Mesh element order
+];
+
+// Define Geometry
+Sphere(1) = {0, 0, 0, radius};
+
+Physical Volume("sphere_volume", 1) = {1}; // Tag the volume
+
+// Define variable mesh size using a MathEval Field
+// Field Formula: a + (b-a) * (1 - Exp(-k*r))
+// Need to handle r=0 case for Sqrt and Exp
+Field[1] = MathEval;
+Field[1].F = Sprintf("%.15g + (%.15g - %.15g) * (1 - Exp(-%.15g * Max(Sqrt(x*x+y*y+z*z), 1e-9)))", coreRes, outerRes, coreRes, kVal);
+
+// Use this field as the background mesh size field
+Background Field = 1;
+
+// Set Mesh Options
+Mesh.ElementOrder = order; // Set the mesh order (1=linear, 2=quadratic, etc.)
+
+// Optional: Optimize high-order elements for better quality
+// Mesh.HighOrderOptimize = 1;
+
+// Optional: Choose 3D meshing algorithm if default isn't good (e.g., 1=MeshAdapt, 4=Frontal, 5=Delaunay, 6=Frontal-Delaunay, 7=MMG3D)
+// Mesh.Algorithm3D = 7;
+
+// Define Physical Groups (optional but good practice)
+// Physical Volume("sphere_volume", 1) = {1}; // Tag the volume
+// Physical Surface("sphere_surface", 2) = {1}; // Tag the boundary surface
\ No newline at end of file
diff --git a/utils/meshGeneration/sphere.mesh b/utils/meshGeneration/sphere.mesh
new file mode 100644
index 0000000..abb1869
--- /dev/null
+++ b/utils/meshGeneration/sphere.mesh
@@ -0,0 +1,261 @@
+MFEM mesh v1.0
+
+dimension
+2
+
+elements
+80
+1 2 0 16 12 53 137 159
+1 2 16 5 18 71 83 153
+1 2 16 18 12 153 51 137
+1 2 12 18 1 51 112 73
+1 2 0 14 16 45 106 53
+1 2 14 3 25 93 110 111
+1 2 14 25 16 111 147 106
+1 2 16 25 5 147 72 71
+1 2 0 13 14 123 74 45
+1 2 13 2 21 88 135 66
+1 2 13 21 14 66 82 74
+1 2 14 21 3 82 84 93
+1 2 0 15 13 133 161 123
+1 2 15 4 22 108 95 127
+1 2 15 22 13 127 151 161
+1 2 13 22 2 151 89 88
+1 2 0 12 15 159 79 133
+1 2 12 1 17 73 56 92
+1 2 12 17 15 92 145 79
+1 2 15 17 4 145 120 108
+1 2 1 18 19 112 48 65
+1 2 18 5 30 83 54 60
+1 2 18 30 19 60 142 48
+1 2 19 30 8 142 143 132
+1 2 5 25 31 72 77 141
+1 2 25 3 27 110 150 57
+1 2 25 27 31 57 75 77
+1 2 31 27 10 75 46 67
+1 2 3 21 26 84 129 62
+1 2 21 2 23 135 144 155
+1 2 21 23 26 155 94 129
+1 2 26 23 7 94 68 43
+1 2 2 22 24 89 158 99
+1 2 22 4 29 95 85 139
+1 2 22 29 24 139 146 158
+1 2 24 29 11 146 115 134
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diff --git a/utils/meshGeneration/sphere.vtk b/utils/meshGeneration/sphere.vtk
new file mode 100644
index 0000000..5b1db21
--- /dev/null
+++ b/utils/meshGeneration/sphere.vtk
@@ -0,0 +1,7979 @@
+# vtk DataFile Version 2.0
+sphere, Created by Gmsh 4.13.1 
+ASCII
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diff --git a/utils/meshGeneration/sphere.vtu b/utils/meshGeneration/sphere.vtu
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diff --git a/utils/meshGeneration/sphere_order2.msh b/utils/meshGeneration/sphere_order2.msh
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+$EndElements
diff --git a/utils/meshGeneration/sphere_order2.vtk b/utils/meshGeneration/sphere_order2.vtk
new file mode 100644
index 0000000..d73a6f8
--- /dev/null
+++ b/utils/meshGeneration/sphere_order2.vtk
@@ -0,0 +1,2317 @@
+# vtk DataFile Version 2.0
+sphere, Created by Gmsh 4.13.1 
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