The main purpose of this paper is to incorporate a refined hysteresis model, viz. a vector Preisach model, in 2D magnetic field computations. To this end the governing Maxwell equations are rewritten in a suitable way, which allows to take into account the proper magnetic material parameters and, moreover, to pass to a variational formulation. The variational problem is solved numerically by a FE approximation, using a quadratic mesh, followed by the time discretisation based upon a modified Cranck Nicholson algorithm. The latter includes a suitable iteration procedure to deal with the nonlinear hysteresis behaviour. Finally, the effectiveness of the presented mathematical tool has been confirmed by several numerical experiments.

Luc R. Dupré, Roger Van Keer, Jan A. A. Melkebeek.
A 2D finite element procedure for magnetic field analysis taking into account a vector Preisach model,
Mathematical Problems in Engineering,
DOI: 10.1155/S1024123X97000574