Comptes Rendus
no. 13-14
Numerical Analysis
Aitken's acceleration of the Restricted Additive Schwarz preconditioning using coarse approximations on the interface
[Accélération de Aitken du préconditionnement Schwarz Additif Restreint utilisant des approximations grossières de l'interface]

Présenté par : Olivier Pironneau

Thomas Dufaud1 ; Damien Tromeur-Dervout1
1 Université de Lyon, université Lyon 1, CNRS, institut Camille-Jordan, 43, boulevard du 11 Novembre 1918, 69622 Villeurbanne cedex, France
Comptes Rendus. Mathématique, Volume 348 (2010) no. 13-14, pp. 821-824.

Une amélioration du préconditionneur Schwarz Additif Restreint (RAS) fondée sur l'accélération de la convergence purement linéaire de la méthode de Schwarz par la méthode de Aitken, est proposée. Sa performance est comparée au préconditionneur RAS sur le problème de Helmholtz bidimensionnel.

An enhancement of the restricted Additive Schwarz (RAS) preconditioning, based on the Aitken's acceleration of the convergence of the Schwarz method, is proposed. Its numerical performance is compared with the RAS preconditioning on the two dimensional Helmholtz problem.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.06.021
Thomas Dufaud 1 ; Damien Tromeur-Dervout 1

1 Université de Lyon, université Lyon 1, CNRS, institut Camille-Jordan, 43, boulevard du 11 Novembre 1918, 69622 Villeurbanne cedex, France 
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Thomas Dufaud; Damien Tromeur-Dervout. Aitken's acceleration of the Restricted Additive Schwarz preconditioning using coarse approximations on the interface. Comptes Rendus. Mathématique, Volume 348 (2010) no. 13-14, pp. 821-824. doi : 10.1016/j.crma.2010.06.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.06.021/

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[7] Z. Li; Y. Saad SchurRAS: A restricted version of the overlapping Schur complement preconditioner, SIAM J. Sci. Comput., Volume 27 (2006) no. 5, pp. 1787-1801

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[10] D. Tromeur-Dervout Meshfree Adaptive Aitken–Schwarz domain decomposition with application to Darcy flow (B.H.V. Topping; P. Ivnyi, eds.), Parallel, Distributed and Grid Computing for Engineering, Saxe-Coburg Publications, Stirlingshire, UK, 2009, pp. 217-250 (Chapter 11, doi:10.4203/csets.21.11)

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