Abstract
In this paper we review a number of auxiliary space based preconditioners for the second order deflnite and semi-deflnite Maxwell problems discretized with the lowest order Nedelec flnite 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.
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