Set up a magnetic symmetry boundary condition:

Set up a magnetic symmetry boundary condition in 3D:

Model an iron cube embedded in air and emerged in a homogeneous magnetic field of [] directed along the axis. The domain is composed of an iron cube of length []. Due to symmetry, only 1/8 of the whole domain is simulated. The air boundary surrounding the iron cube is modeled as a second cube of length [].

In the reduced geometry, at the surfaces parallel to the planes - and - a symmetry boundary condition needs to be applied.

Define the mesh:

The mesh has internal boundaries that represent the inner iron cube. Define the iron cube:

Visualize a wireframe of the mesh:

Define variables:

Define parameters the permeability of vacuum and iron :

To specify the homogeneous magnetic field across the domain, an outward magnetic flux density normal to the boundary at is specified.

Set up the magnetic flux density condition:

Set up the magnetic symmetry condition:

Since the magnetic symmetry condition is a Neumann zero boundary condition, which is the default boundary condition if nothing is specified on a boundary, it could also be omitted.

Solve the magnetostatic PDE model:

Compute the magnetic field intensity:

To visualize another 1/8 of the field, at , the symmetric behavior of the field must be considered. At positive values, the field is and at negative values, the field is .

Visualize the symmetric vector field at of the complete geometry: