Vector potential formulation for magnetostatics and modelling of permanent magnets

A very general magnetostatic problem involving inhomogeneous anisotropic materials filling irregular regions and with mixed boundary conditions is formulated in terms of magnetic vector potential. Some restrictions inherent to the introduction of a vector potential become apparent and additional conditions for the uniqueness of the vector potential naturally arise. The modelling of permanent magnets is introduced in both the vector potential and the field formulations by weakening the regularity requirements on the source term. The vector potential formulation is also shown to be equivalent to a penalized formulation widely used in numerical applications.