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

Stephan Willerich, Hans Georg Herzog

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 languageEnglish
Pages (from-to)1584-1594
Number of pages11
JournalCOMPEL - The international journal for computation and mathematics in electrical and electronic engineering
Volume38
Issue number5
DOIs
StatePublished - 21 Oct 2019

Keywords

  • Electromagnetic fields
  • Finite element method
  • Magnetic hysteresis

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