École Nationale Supérieure de
Techniques Avancées

Abstract

The H-based variational formulation for the magneto-quasistatic eddy current model relies on functions in H(curl, Ω) with vanishing rotation in the non-conducting region ΩI . In ΩI such functions can be represented by means of scalar magnetic potentials provided that the first Betti number β1(ΩI) of ΩI vanishes, that is, ΩI has no handles. Otherwise, the use of scalar potentials entails introducing cuts Σ, such that β1(ΩI \ Σ = 0). Generically, the H-based boundary element formulation of the eddy current model involves boundary integral equations (BIEs) posed on ∂ΩI∪Ω, though the cuts contribute only a minimal amount of information, a single scalar per connected component. We investigate modifications of those BIE, which no longer rely on cuts as integration domains and only need knowledge of boundaries of cuts. For Galerkin BEM this has the big benefit that we can dispense with both construction and meshing of cuts; boundaries of cuts are just closed curves and can be built and handled much more easily.