This paper was produced for the 2019 NAFEMS World Congress in Quebec Canada

Resource Abstract

The numerical analysis of electrical devices by means of Finite Element Methods (FEM) is often hindered by the need to incorporate the surrounding air. Next to the complexity of the discretisation of the air region, this exterior region has to be truncated by artificial boundaries and thereby incurring a modelling error. Even more problematic are moving parts which require tedious remeshing and remapping techniques. In this work, we take an alternative approach by using the Boundary Element Method (BEM) in conjunction with FEM. Whereas the solid parts of the electrical device are discretised by FEM which can easily account for material non-linearities, the surrounding domain is represented by BEM via a surface-only discretisation. No FEM mesh for the air is thus needed. The errors incurred by above mentioned truncation are avoided and the individual parts can freely move with respect to each other without deforming a FEM mesh.



Nevertheless, the use of BEM comes at a price: singular integrals and fully-populated system matrices render a naive implementation of the method useless for practical purposes. We will address these issues and present an implementation that is robust and –by means of a fast multipole approximation– exhibits linear complexity in storage size and execution time. Several documented benchmark problems demonstrate the accuracy and versatility of the presented method. Finally, we present some multiphysics examples such as induction heating and eddy-current brakes.