An efficient numerical scheme for the FE-approximation of magnetic stray fields in infinite domains

• Published in: Computational mechanics Vol. 70; no. 1; pp. 141 - 153
• Main Authors: Schröder, Jörg, Reichel, Maximilian, Birk, Carolin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2022; Springer; Springer Nature B.V
• Subjects: Approximation; Classical and Continuum Physics; Computational Science and Engineering; Domains; Engineering; Exact solutions; Magnetostatics; Original Paper; Theoretical and Applied Mechanics; Topology; Static condensation; Finite elements; Infinite/unbounded domain; Magnetostatics
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-022-02162-1

In this contribution we propose an efficient and simple finite-element procedure for the approximation of open boundary problems for applications in magnetostatics. In these problems, the interaction of the solid with external space plays a crucial role because of the magnetic stray fields that arise. For this purpose, the infinite region under consideration is approximated by a sufficiently large domain. This region is then divided into a so-called interior domain and an exterior domain. As an essential prerequisite, we assume linear behavior of the (large) exterior domain. The latter is then reduced to the degrees of freedom of the connecting line (2D)/connecting surface (3D) of both domains via static condensation. The proposed finite element scheme can be seen as an alternative to established methods for infinite domains. These methods often require semi-analytical solutions to describe the behavior in the exterior domain, which can be difficult to obtain if heterogeneous structures are present. The proposed finite element procedure is not subject to any restrictions with regard to the topology of the exterior space. After a general introduction of the numerical scheme, we apply the method to problems of magnetostatics with nonlinear behavior in the interior domain.