A non-smooth Newton method for the solution of magnetostatic field problems with hysteresis

Abstract

Purpose

The use of gradient-based methods in finite element schemes can be prevented by undefined derivatives, which are encountered when modeling hysteresis in constitutive material laws. This paper aims to present a method to deal with this problem.

Design/methodology/approach

Non-smooth Newton methods provide a generalized framework for the treatment of minimization problems with undefined derivatives. Within this paper, a magnetostatic finite element formulation that includes hysteresis is presented. The non-linear equations are solved using a non-smooth Newton method.

Findings

The non-smooth Newton method shows promising convergence behavior when applied to a model problem. The numbers of iterations for magnetization curves with and without hysteresis are within the same range.

Originality/value

Mathematical tools like Clarke's generalized Jacobian are applied to magnetostatic field problems with hysteresis. The relation between the non-smooth Newton method and other methods for solving non-linear systems with hysteresis like the M(B)-iteration is established.

Citation

Willerich, S. and Herzog, H.-G. (2019), "A non-smooth Newton method for the solution of magnetostatic field problems with hysteresis", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 38 No. 5, pp. 1584-1594. https://doi.org/10.1108/COMPEL-12-2018-0499