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

Stephan Willerich, Hans Georg Herzog

• 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 nonsmooth 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.