Parallel Hierarchical Matrix Preconditioners for the Curl-Curl Operator

Abstract

This paper deals with the preconditioning of the curl-curl operator. We use

$\boldsymbol{H}$(curl)-conforming finite elements for the discretization of our corresponding magnetostatic model problem. Jumps in the material parameters influence the condition of the problem. We will demonstrate by theoretical estimates and numerical experiments that hierarchical matrices are well suited to construct efficient parallel preconditioners for the fast and robust iterative solution of such problems.