Complementary 2-D finite element procedures for the magnetic field analysis using a vector hysteresis model

The main purpose of this paper is to incorporate a re ned hysteresis model, viz., a vector Preisach model, in 2-D magnetic eld computations. Two complementary formulations, based either on the scalar or on the vector potential, are considered. The governing Maxwell equations are rewritten in a suitable way, that allows to take into account the proper magnetic material parameters and, moreover, to pass to a variational formulation. The variational problems are solved numerically by a Finite Element approximation, using a quadratic mesh, followed by a time discretization method based upon a modi ed Cranck{Nicholson algorithm. Finally, the e ectiveness of the presented mathematical tools have been con rmed by several numerical experiments, comparing the complementarity of the two procedures.