Comptes Rendus
no. 9
Numerical Analysis
Domain decomposition methods of dual-primal FETI type for edge element approximations in three dimensions
[Méthodes FETI dual-primal pour approximations aux éléments finis d'arête en dimension trois.]

Présenté par : Olivier Pironneau

Andrea Toselli1
1 Seminar for Applied Mathematics, ETH Zürich, CH-8092 Zürich, Switzerland
Comptes Rendus. Mathématique, Volume 339 (2004) no. 9, pp. 673-678.

Nous considérons des algorithmes FETI pour des approximations en éléments finis d'arête en dimension trois. Nous montrons d'abord qu'il existe un couplage fort entre les degrés de liberté tangentiels associés aux arêtes et aux faces des sous-domaines. Nous proposons ensuite un algorithme FETI dual-primal qui utilise un changement de base et un choix particulier pour le solveur grossier. Nous donnons une borne logarithmique pour le nombre de conditionnement de l'algorithme. Les tests numériques confirment cette borne et la nécessité du changement de base.

We consider domain decomposition algorithms of FETI type for edge element approximations in three dimensions. We first show that a strong coupling exists between tangential degrees of freedom associated to the subdomain edges and faces. We then propose a dual-primal FETI algorithm that relies on a change of basis and on a suitable choice of a coarse space. We give a logarithmic bound for the condition number of the resulting preconditioned operator. Numerical results confirm this bound and the necessity of performing a change of basis.

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Accepté le :
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DOI : 10.1016/j.crma.2004.09.021
Andrea Toselli 1

1 Seminar for Applied Mathematics, ETH Zürich, CH-8092 Zürich, Switzerland 
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     title = {Domain decomposition methods of dual-primal {FETI} type for edge element approximations in three dimensions},
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Andrea Toselli. Domain decomposition methods of dual-primal FETI type for edge element approximations in three dimensions. Comptes Rendus. Mathématique, Volume 339 (2004) no. 9, pp. 673-678. doi : 10.1016/j.crma.2004.09.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.021/

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[3] C. Farhat; M. Lesoinne; P. LeTallec; K. Pierson; D. Rixen FETI-DP: a dual-primal unified FETI method. I. A faster alternative to the two-level FETI method, Int. J. Numer. Methods Engrg., Volume 50 (2001) no. 7, pp. 1523-1544

[4] A. Klawonn; O.B. Widlund; M. Dryja Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients, SIAM J. Numer. Anal., Volume 40 (2002) no. 1, pp. 159-179

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