A non-smooth Newton method for the solution of magnetostatic field problems with hysteresis. Issue 5 (2nd September 2019)

• Record Type: Journal Article
• Authors: Willerich, Stephan; Herzog, Hans-Georg
• Is Part Of: Compel. Volume 38:Issue 5(2019)
• Page Start: 1584
• Page End: 1594
• Publication Date: 2019-09-02
• Subjects: Electromagnetic fields -- Finite element method -- Magnetic hysteresis; Electrical engineering -- Data Processing -- Periodicals; Electrical engineering -- Mathematics -- Periodicals; Electrical engineering -- Periodicals; Electronics -- Data Processing -- Periodicals; Electronics -- Mathematics -- Periodicals; 621.3
• DOI: 10.1108/COMPEL-12-2018-0499
• Languages: English
• ISSNs: 0332-1649

Abstract

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.