Parallel Auxiliary Space AMG for H(Curl) Problems
Tzanio V. Kolev 1, Panayot S. Vassilevski 21 Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P.O. Box 808, L-560, Livermore, CA 94551, USA
2 Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P.O. Box 808, L-560, Livermore, CA 94551, USA
Received 2007-12-19 Revised 2008-7-23 Accepted 2009-2-5 Online 2009-4-27
In this paper we review a number of auxiliary space based preconditioners for the second order definite and semi-definite Maxwell problems discretized with the lowest order Nedelec finite elements. We discuss the parallel implementation of the most promising of these methods, the ones derived from the recent Hiptmair-Xu (HX) auxiliary space decomposition [Hiptmair and Xu, SIAM J. Numer. Anal., 45 (2007), pp. 2483-2509]. An extensive set of numerical experiments demonstrate the scalability of our implementation on large-scale H(curl) problems.
Key words: Parallel algebraic multigrid, H(curl) problems, Edge elements, Auxiliary space preconditioning.
AMS subject classifications: 65F10, 65N30, 65N55.
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