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

• Stephan Willerich ^[1] ; Hans-Georg Herzog ^[1]
  1. [1] Technical University Munich

     Technical University Munich

     Kreisfreie Stadt München, Alemania

     
• Localización: Compel: International journal for computation and mathematics in electrical and electronic engineering, ISSN 0332-1649, Vol. 38, Nº 5, 2019, págs. 1584-1594
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.