Solving generalized eigenvalue problems on the interfaces to build a robust two-level FETI method

Nicole Spillane; Victorita Dolean; Patrice Hauret; Frédéric Nataf; Daniel J. Rixen

doi:10.1016/j.crma.2013.03.010

Partial Differential Equations/Numerical Analysis

Solving generalized eigenvalue problems on the interfaces to build a robust two-level FETI method
[Une grille grossière robuste pour FETI grâce à la résolution de problèmes aux valeurs propres généralisés sur les interfaces]

Présenté par : the Editorial Board

Nicole Spillane ^1,² ; Victorita Dolean ³ ; Patrice Hauret ² ; Frédéric Nataf ¹ ; Daniel J. Rixen ⁴

¹ Laboratoire Jacques-Louis-Lions, UMR 7598, université Pierre-et-Marie-Curie (Paris 6), 75252 Paris cedex 05, France
² Michelin Technology Center, place des Carmes-Déchaux, 63000 Clermont-Ferrand, France
³ Laboratoire Jean-Alexandre-Dieudonné, UMR 6621, université de Nice–Sophia Antipolis, 06108 Nice cedex 02, France
⁴ Institute of Applied Mechanics, TU München, 85747 Garching, Germany

Comptes Rendus. Mathématique, Volume 351 (2013) no. 5-6, pp. 197-201.

Résumé
Abstract

La méthode FETI a demontré son efficacité et sa compétitivité sur de nombreux problèmes industriels. Un désavantage est que ses performances dépendent fortement de la distribution des coefficients dans les équations. Ceci est en quelque sorte confirmé par le fait que lʼanalyse théorique requiert des hypothèses sur ces coefficients et le partitionnement. Nous proposons ici la construction dʼun espace grossier telle que le taux de convergence de la méthode à deux niveaux soit garanti sans hypothèses supplémentaires. Cette construction repose sur lʼidentification des modes problématiques grâce à la résolution de problèmes aux valeurs propres généralisés.

FETI is a very popular method, which has proved to be extremely efficient on many large-scale industrial problems. One drawback is that it performs best when the decomposition of the global problem is closely related to the parameters in equations. This is somewhat confirmed by the fact that the theoretical analysis goes through only if some assumptions on the coefficients are satisfied. We propose here to build a coarse space for which the convergence rate of the two-level method is guaranteed regardless of any additional assumptions. We do this by identifying the problematic modes using generalized eigenvalue problems.

Reçu le : 2012-11-23
Accepté le : 2013-03-18
Publié le : 2013-03-01

DOI : 10.1016/j.crma.2013.03.010

Affiliations des auteurs :

Nicole Spillane ^{1, 2} ; Victorita Dolean ³ ; Patrice Hauret ² ; Frédéric Nataf ¹ ; Daniel J. Rixen ⁴

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     author = {Nicole Spillane and Victorita Dolean and Patrice Hauret and Fr\'ed\'eric Nataf and Daniel J. Rixen},
     title = {Solving generalized eigenvalue problems on the interfaces to build a robust two-level {FETI} method},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {197--201},
     publisher = {Elsevier},
     volume = {351},
     number = {5-6},
     year = {2013},
     doi = {10.1016/j.crma.2013.03.010},
     language = {en},
}

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Nicole Spillane; Victorita Dolean; Patrice Hauret; Frédéric Nataf; Daniel J. Rixen. Solving generalized eigenvalue problems on the interfaces to build a robust two-level FETI method. Comptes Rendus. Mathématique, Volume 351 (2013) no. 5-6, pp. 197-201. doi : 10.1016/j.crma.2013.03.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.03.010/

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