Domain decomposition methods of dual-primal FETI type for edge element approximations in three dimensions

Andrea Toselli

doi:10.1016/j.crma.2004.09.021

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 Toselli ¹

¹ Seminar for Applied Mathematics, ETH Zürich, CH-8092 Zürich, Switzerland

Comptes Rendus. Mathématique, Volume 339 (2004) no. 9, pp. 673-678.

Résumé
Abstract

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.

Reçu le : 2004-09-08
Accepté le : 2004-09-21
Publié le : 2004-10-27

DOI : 10.1016/j.crma.2004.09.021

Affiliations des auteurs :

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},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {673--678},
     publisher = {Elsevier},
     volume = {339},
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     year = {2004},
     doi = {10.1016/j.crma.2004.09.021},
     language = {en},
}

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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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