Normal Magnetic Field Condition¶

The normal magnetic field condition is a boundary condition given by

\[ \left. \tilde{\mathbf{H}} \times \mathbf{n} \right|_{\Gamma} = 0, \]

which forces the magnetic field $\tilde{\mathbf{H}}$ to be normal to the boundary $\Gamma$ — its tangential component vanishes. It is the natural boundary condition of the A-formulation: no constraint is applied; the corresponding surface term in the weak form simply vanishes. A boundary left without any condition therefore behaves as a normal magnetic field boundary.

Figure 1: The magnetic field meets the boundary $\Gamma$ at a right angle; its tangential component vanishes ($\tilde{\mathbf{H}} \times \mathbf{n} = 0$).

Applicability¶

Applicable on boundary surfaces. It is the natural boundary condition of the A-formulation, so it adds no constraint and no weak-form term — a boundary left without any condition behaves identically. Apply it explicitly to mark field-normal symmetry planes or idealized high-permeability interfaces. The condition takes no parameters.

When to use this¶

Symmetry planes where the field is perpendicular to the cut plane (e.g. the mid-plane between two opposing magnets, or the equatorial plane of an axially excited solenoid).
Idealized iron interface. A region of very high permeability forces the field to be perpendicular at its surface ($\mu_r \to \infty$ implies $\mathbf{H} \times \mathbf{n} \to 0$); use this when modelling the surrounding air without meshing the iron interior.

Usage¶

from mufem.electromagnetics.timeharmonicmagnetic import (
    NormalMagneticFieldBoundaryCondition,
)

normal_field_bc = NormalMagneticFieldBoundaryCondition(
    name="Symmetry",
    marker="Symmetry" @ Bnd,
)

time_harmonic_magnetic_model.add_condition(normal_field_bc)