Theoretical and numerical difficulties in 3-D vector potential methods in finite element magnetostatic computations

The results of the application of three well-known 3-D magnetic vector potential (MVP)-based finite-element formulations for computation of magnetostatic fields in electrical devices are discussed. The three methods were identically applied to three practical examples, the first of which contained only one medium (free space), while the second and third examples contained a mix of free space and iron. The first of these methods is based on the unconstrained curl-curl of the MVP, while the second and third methods are predicated upon constraining the divergence of the MVP to zero (Coulomb´s gauge). It was found that the two latter methods cease to give useful and meaningful results when the global solution region contains a mix of media of high and low permeabilities. Furthermore, it was found that their results do not achieve the intended zero constraint on the divergence of the MVP