Parallel Auxiliary Space AMG for $\boldsymbol{H}$(Curl) Problems
DOI:
https://doi.org/10.4208/jcm.2009.27.5.013Keywords:
Parallel algebraic multigrid, H(curl) problems, Edge elements, Auxiliary space preconditioning.Abstract
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 Nédélec 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 $\boldsymbol{H}$(curl) problems.