A highly scalable multigrid method with parallel direct coarse grid solver for Maxwell’s equations

Abstract

We present scalability results on the cluster HERMIT of a parallel direct solver for finite element methods. This is applied in a multigrid iteration to obtain a highly scalable solution method for the computation of reliable and exact approximations of electro-magnetic fields in the cavity problem for the Maxwell’s equations, and of electromagnetic eigenfrequencies in Maxwell’s eigenvalue problem. Here, we consider in particular the case that several frequencies has to be determined simultaneously. For both problems a Laplace equation has to be solved in addition in order to obtain divergence-free fields.