Magnetostatics — Magnetic Field, Inductance & Permanent Magnets

Why do we use vector potential A instead of B directly in magnetostatic FEM?

Writing B = curl(A) automatically satisfies the divergence-free condition (no magnetic monopoles) without enforcing it separately. The field equation for A is more amenable to standard Galerkin FEM discretization, and boundary conditions on A are simpler to apply than on B directly.

How do you handle nonlinear magnetic materials (saturation) in magnetostatic FEM?

Start with initial permeability mu, solve the linear problem, update mu at each element from the computed field on the nonlinear B-H curve, resolve. This Newton-Raphson or Picard iteration continues until B-H consistency is achieved everywhere. Usually converges in 5-15 iterations unless deep saturation occurs.