TY  - JOUR
AB  - 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.
VL  - 38
IS  - 5
SN  - 0332-1649
DO  - 10.1108/COMPEL-12-2018-0499
UR  - https://doi.org/10.1108/COMPEL-12-2018-0499
AU  - Willerich Stephan
AU  - Herzog Hans-Georg
PY  - 2019
Y1  - 2019/01/01
TI  - A non-smooth Newton method for the solution of magnetostatic field problems with hysteresis
T2  - COMPEL - The international journal for computation and mathematics in electrical and electronic engineering
PB  - Emerald Publishing Limited
SP  - 1584
EP  - 1594
Y2  - 2024/04/23
ER  -