Magnetostatic simulations with consideration of exterior domains using the scaled boundary finite element method

Abstract

In this work we propose a hybrid SBFEM-FEM approach for the efficient calculation of magnetic stray fields in unbounded domains. In magnetostatic boundary value problems, the interaction between the magnetic solid, externally applied magnetic fields and the surrounding exterior domain is of crucial importance. This interaction generates the magnetic stray field, which diminishes in intensity with increasing distance to the solid. For this reason, the overall infinite domain is simulated using a hybrid formulation of the scaled boundary finite element method (SBFEM) and the finite element method. To this end, the entire domain is divided into a finite and an infinite sub-region, referred to as the interior and the exterior domain. While the interior domain is modeled using finite elements, the exterior domain is reduced onto the boundary of the interior domain by using the SBFEM. The latter provides a semi-analytical solution of the considered magnetostatic problem in an unbounded domain, where the externally applied magnetic fields are taken into account. The advantage of this method is the rigorous representation of the surrounding exterior domain without an explicit discretization. Compared to completely discretized systems, significantly better results can be obtained with smaller systems of equations.