refactor(meshGeneration): working on gmsh to generate curvilinear isogeomatric spherical mesh

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}")