Mirror Symmetry in Integral Formulations for Eddy Currents

This contribution addresses the exploitation of mirror symmetry (formally, the abelian D₁ and D₂ dihedral symmetry groups) in various integral formulations for eddy current problems. The novelty of the contribution is in particular how to rigorously treat non-simply-connected conductors when computing the first cohomology group generators on the symmetry cell of the problem only.

I. Introduction

Exploiting symmetry has been recognized as an effective method to save a sensible amount of simulation time. It allows to solve the problem on a given domain by solving a family of problems on a symmetry cell instead. It is impossible to survey all the literature, so we just mention [1] for the finite element method (FEM) and [2] for a FEM–boundary element method (FEM–BEM) based on the magnetic vector potential.