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Volume 27, Issue 5
Parallel Auxiliary Space AMG for $\boldsymbol{H}$(Curl) Problems

Tzanio V. Kolev & Panayot S. Vassilevski

DOI: 10.4208/jcm.2009.27.5.013

J. Comp. Math., 27 (2009), pp. 604-623.

Published online: 2009-10

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  • 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.

  • Keywords

Parallel algebraic multigrid, H(curl) problems, Edge elements, Auxiliary space preconditioning.

  • AMS Subject Headings

65F10, 65N30, 65N55.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-27-604, author = {}, title = {Parallel Auxiliary Space AMG for $\boldsymbol{H}$(Curl) Problems}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {5}, pages = {604--623}, 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.27.5.013}, url = {http://global-sci.org/intro/article_detail/jcm/8592.html} }
TY - JOUR T1 - Parallel Auxiliary Space AMG for $\boldsymbol{H}$(Curl) Problems 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 -

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.

Tzanio V. Kolev & Panayot S. Vassilevski. (2019). Parallel Auxiliary Space AMG for $\boldsymbol{H}$(Curl) Problems. Journal of Computational Mathematics. 27 (5). 604-623. doi:10.4208/jcm.2009.27.5.013
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