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.
Original language | English |
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Pages (from-to) | 1584-1594 |
Number of pages | 11 |
Journal | COMPEL - The international journal for computation and mathematics in electrical and electronic engineering |
Volume | 38 |
Issue number | 5 |
DOIs | |
State | Published - 21 Oct 2019 |
Keywords
- Electromagnetic fields
- Finite element method
- Magnetic hysteresis