Mathematical Problems in Engineering
Volume 3 (1997), Issue 3, Pages 267-286

A 2D finite element procedure for magnetic field analysis taking into account a vector Preisach model

Luc R. Dupré,1 Roger Van Keer,2 and Jan A. A. Melkebeek1

1Department of Electrical Power Engineering, University of Gent, Sint-Pietersnieuwstraat 41, Gent B-9000, Belgium
2Department of Mathematical Analysis, University of Gent, Galglaan 2, Gent B-9000, Belgium

Received 1 July 1996

Copyright © 1997 Luc R. Dupré et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.