Parallel Hierarchical Matrix Preconditioners for the Curl-Curl Operator

Abstract
This paper deals with the preconditioning of the curl-curl operator. We use H(curl)- conforming flnite elements for the discretization of our corresponding magnetostatic model problem. Jumps in the material parameters in∞uence the condition of the problem. We will demonstrate by theoretical estimates and numerical experiments that hierarchical matrices are well suited to construct e-cient parallel preconditioners for the fast and robust iterative solution of such problems.

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