Multiscale Finite Element Method for Laminated Domains in Electrical Engineering

Abstract

The multiscale finite element method (MSFEM) is very promising to solve eddy current problems (ECPs) in laminated iron cores of electrical devices accurately with minimum computational effort. First, MSFEM is introduced in a very simple one-dimensional elliptic problem which is then extended to the corresponding two-dimensional one. The averaging of the highly oscillating material parameters is described. The use of a triangular mesh is studied. Static condensation in the context of MSFEM is also shown. This work aims at solving ECPs in two dimensions based on either a current vector potential T or a magnetic vector potential A. Multiscale approaches for T and A are constructed and explained. The multiscale approaches are justified by the analytical solutions of eddy currents in an infinite slab. Particular attention is paid to the correct modeling of the edge effect. The excellent performance of higher order MSFEM for small penetration depths is shown.