Comptes Rendus
no. S1
Recent advances in domain decomposition methods for large-scale saddle point problems
[Progrès récents dans les méthodes de décomposition de domaine pour le problème du point de selle à grande échelle]
Frédéric Nataf1   ; Pierre-Henri Tournier1 
1 Laboratoire J.L. Lions, Sorbonne Université, 4 place Jussieu, France
Comptes Rendus. Mécanique, Online first (2022), pp. 1-15.

L’extensibilité des solveurs parallèles pour les problèmes à forte hétérogénéité repose sur des espaces grossiers adaptatifs construits à partir de problèmes de valeurs propres généralisés dans les sous-domaines. La théorie correspondante est puissante et flexible mais le développement d’une implémentation parallèle efficace est un défi. Nous présentons ici les avancées récentes en matière d’espaces grossiers adaptatifs et leurs implémentations open source dans des langages spécifiques au domaine tels que FreeFem, en nous concentrant sur une nouvelle décomposition de domaine pour les formulations de points de selle avec des tests numériques.

Scalability of parallel solvers for problems with high heterogeneities relies on adaptive coarse spaces built from generalized eigenvalue problems in the subdomains. The corresponding theory is powerful and flexible but the development of an efficient parallel implementation is challenging. We report here on recent advances in adaptive coarse spaces and on their open source implementations in domain specific languages such as FreeFem, focusing on a new domain decomposition for saddle point formulations with some numerical tests.

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DOI : 10.5802/crmeca.130
Keywords: High performance computing, Saddle point problem, Domain decomposition methods, Nearly incompressible elasticity, Multilevel methods
Mot clés : Calcul haute performance, Problème de point selle, Méthodes de décomposition de domaine, Elasticité presque incompressible, Méthode multi niveaux
Frédéric Nataf 1 ; Pierre-Henri Tournier 1

1 Laboratoire J.L. Lions, Sorbonne Université, 4 place Jussieu, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     year = {2022},
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Frédéric Nataf; Pierre-Henri Tournier. Recent advances in domain decomposition methods for large-scale saddle point problems. Comptes Rendus. Mécanique, Online first (2022), pp. 1-15. doi : 10.5802/crmeca.130.

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