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Volume 27, Issue 5
Parallel Hierarchical Matrix Preconditioners for the Curl-Curl Operator

Mario Bebendorf & Joerg Ostrowski

DOI: 10.4208/jcm.2009.27.5.014

J. Comp. Math., 27 (2009), pp. 624-641.

Published online: 2009-10

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  • Abstract

This paper deals with the preconditioning of the curl-curl operator. We use

$\boldsymbol{H}$(curl)-conforming finite elements for the discretization of our corresponding magnetostatic model problem. Jumps in the material parameters influence the condition of the problem. We will demonstrate by theoretical estimates and numerical experiments that hierarchical matrices are well suited to construct efficient parallel preconditioners for the fast and robust iterative solution of such problems.

  • Keywords

Computational electromagnetism, Preconditioners, Hierarchical matrices, Parallelization.

  • AMS Subject Headings

65N22, 65F10, 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-624, author = {Mario Bebendorf and Joerg Ostrowski}, title = {Parallel Hierarchical Matrix Preconditioners for the Curl-Curl Operator}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {5}, pages = {624--641}, abstract = {

This paper deals with the preconditioning of the curl-curl operator. We use

$\boldsymbol{H}$(curl)-conforming finite elements for the discretization of our corresponding magnetostatic model problem. Jumps in the material parameters influence the condition of the problem. We will demonstrate by theoretical estimates and numerical experiments that hierarchical matrices are well suited to construct efficient parallel preconditioners for the fast and robust iterative solution of such problems.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.27.5.014}, url = {http://global-sci.org/intro/article_detail/jcm/8593.html} }
TY - JOUR T1 - Parallel Hierarchical Matrix Preconditioners for the Curl-Curl Operator AU - Mario Bebendorf & Joerg Ostrowski JO - Journal of Computational Mathematics VL - 5 SP - 624 EP - 641 PY - 2009 DA - 2009/10 SN - 27 DO - http://doi.org/10.4208/jcm.2009.27.5.014 UR - https://global-sci.org/intro/article_detail/jcm/8593.html KW - Computational electromagnetism, Preconditioners, Hierarchical matrices, Parallelization. AB -

This paper deals with the preconditioning of the curl-curl operator. We use

$\boldsymbol{H}$(curl)-conforming finite elements for the discretization of our corresponding magnetostatic model problem. Jumps in the material parameters influence the condition of the problem. We will demonstrate by theoretical estimates and numerical experiments that hierarchical matrices are well suited to construct efficient parallel preconditioners for the fast and robust iterative solution of such problems.

Mario Bebendorf and Joerg Ostrowski. (2009). Parallel Hierarchical Matrix Preconditioners for the Curl-Curl Operator. Journal of Computational Mathematics. 27 (5). 624-641. doi:10.4208/jcm.2009.27.5.014
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