Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

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

A non-smooth Newton method for the solution of magnetostatic field problems with hysteresis 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/approachNon-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.FindingsThe 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/valueMathematical 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: Theinternational Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

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

Loading next page...
 
/lp/emerald-publishing/a-non-smooth-newton-method-for-the-solution-of-magnetostatic-field-kbTRlaNJiU
Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
0332-1649
DOI
10.1108/compel-12-2018-0499
Publisher site
See Article on Publisher Site

Abstract

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/approachNon-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.FindingsThe 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/valueMathematical 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.

Journal

COMPEL: Theinternational Journal for Computation and Mathematics in Electrical and Electronic EngineeringEmerald Publishing

Published: Oct 21, 2019

Keywords: Electromagnetic fields; Finite element method; Magnetic hysteresis

References