J. Comp. Math., 27 (2009), pp. 624-641.

Parallel Hierarchical Matrix Preconditioners for the Curl-Curl Operator

Mario Bebendorf 1, Joerg Ostrowski 2

1 Institut fur Numerische Simulation, Universitat Bonn, Wegelerstrasse 6, 53115 Bonn, Germany
2 ABB Switzerland Ltd, Corporate Research, Segelhofstrasse 1 K / P.O. Box, CH-5405 Baden 5 Dattwil

Received 2008-3-1 Revised 2008-10-14 Accepted 2009-2-5 Online 2009-4-27


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

Key words: Computational electromagnetism, Preconditioners, Hierarchical matrices, Parallelization.

AMS subject classifications: 65N22, 65F10, 65N30.

Email: bebendorf@ins.uni-bonn.de, joerg.ostrowski@ch.abb.com

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