TY - JOUR
T1 - Parallel Auxiliary Space AMG for $\boldsymbol{H}$(Curl) Problems
AU - Tzanio V. Kolev  & Panayot S. Vassilevski
JO - Journal of Computational Mathematics
VL - 5
SP - 604
EP - 623
PY - 2009
DA - 2009/10
SN - 27
DO - http://doi.org/10.4208/jcm.2009.27.5.013
UR - https://global-sci.org/intro/article_detail/jcm/8592.html
KW - Parallel algebraic multigrid, H(curl) problems, Edge elements, Auxiliary space
preconditioning.
AB - <p style="text-align: justify;">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 $\boldsymbol{H}$(<strong>curl</strong>) problems.</p>