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.
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.
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.
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.
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
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