Finite Element

The first and most crucial step in finite element micromagnetics is mesh generation. Several software tools are available for mesh generation. Here we introduce two primary options:

1. Netgen

• Repository: https://github.com/NGSolve/netgen

• Documentation: https://github.com/NGSolve/netgen/blob/master/doc/ng4.pdf

Typical Usage (creates hemisphere):

algebraic3d

solid hemisphere = sphere (1, 0, 0; 10) and plane (1, 0, 0; 0, 0, -1);

tlo hemisphere -maxh=2.0;

MicroMagnetic.jl natively supports Netgen's Neutral format.

2. Gmsh

• Website: https://gmsh.info/

• Tutorial: https://gmsh.info/dev/doc/texinfo/gmsh.html#Gmsh-tutorial

Gmsh supports OpenCASCADE geometry kernel, enabling direct creation of complex shapes. Below is a modified Julia example generating the same hemisphere and exporting to Gmsh format:

using Gmsh

gmsh.initialize()
gmsh.model.add("hemisphere")

# Create sphere and cutting box
sphere_tag = gmsh.model.occ.addSphere(1, 0, 0, 10)
box_tag = gmsh.model.occ.addBox(-100, -100, 0, 200, 200, 100)  # Large cutting box

# Perform boolean cut operation
hemisphere, _ = gmsh.model.occ.cut(
    [(3, sphere_tag)],  # Original sphere (dim=3)
    [(3, box_tag)]      # Cutting tool (dim=3)
)
gmsh.model.occ.synchronize()

# Generate mesh with size constraints
gmsh.option.setNumber("Mesh.MeshSizeMax", 2.0)
gmsh.model.mesh.generate(3)

# Export in Gmsh format
gmsh.write("hemisphere.msh")
gmsh.write("hemisphere.vtk")
gmsh.finalize()

The vtk file can be opened using Paraview, as follows: