Comptes Rendus
Numerical Analysis
Non-overlapping additive Schwarz methods tuned to highly heterogeneous media
Comptes Rendus. Mathématique, Volume 341 (2005) no. 11, pp. 701-705.

In this Note an improved version of the Schwarz domain decomposition method is introduced for highly heterogeneous media. This method uses new optimized interface conditions specially designed to take into account the heterogeneity between the subdomains on the interfaces. The mathematical analysis of these interface conditions is first presented. Then the asymptotic analysis upon the mesh size parameter together with the heterogeneity ratio is detailed.

Dans cette Note une variante de l'algorithme de Schwarz est introduite pour des milieux très hétérogènes. Cette méthode utilise des conditions d'interfaces optimisées spécialement conçues pour tenir compte de l'hétérogénéité entre les sous-domaines. L'étude mathématique de ces conditions d'interfaces est dans un premier temps présentée. Une analyse asymptotique en fonction de la finesse du maillage et du rapport de l'hétérogénéité est ensuite détaillée.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.09.032
Yvon Maday 1, 2; Frédéric Magoulès 3

1 Laboratoire Jacques-Louis Lions, université Pierre et Marie Curie, BP 187, 75252 Paris cedex 05, France
2 Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA
3 Institut Elie-Cartan de Nancy, université Henri-Poincaré, BP 239, 54506 Vandoeuvre-les-Nancy cedex, France
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Yvon Maday; Frédéric Magoulès. Non-overlapping additive Schwarz methods tuned to highly heterogeneous media. Comptes Rendus. Mathématique, Volume 341 (2005) no. 11, pp. 701-705. doi : 10.1016/j.crma.2005.09.032. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.09.032/

[1] P. Chevalier; F. Nataf Symmetrized method with optimized second-order conditions for the Helmholtz equation, Domain Decomposition Methods, 10, Boulder, CO, 1997, Amer. Math. Soc., Providence, RI, 1998, pp. 400-407

[2] F. Collino; S. Ghanemi; P. Joly Domain decomposition methods for harmonic wave propagation: a general presentation, Comput. Methods Appl. Mech. Engrg., Volume 2 (2000) no. 4, pp. 171-211

[3] B. Després Domain decomposition method and the Helmholtz problem. II, Second International Conference on Mathematical and Numerical Aspects of Wave Propagation, Newark, DE, 1993, SIAM, Philadelphia, PA, 1993, pp. 197-206

[4] V. Dolean; S. Lanteri; F. Nataf Construction of interface conditions for solving compressible Euler equations by non-overlapping domain decomposition methods, Int. J. Numer. Methods Fluids, Volume 40 (2002), pp. 1485-1492

[5] M.J. Gander; L. Halpern; F. Nataf Optimized Schwarz methods (T. Chan; T. Kako; H. Kawarada; O. Pironneau, eds.), Twelfth International Conference on Domain Decomposition Methods, Chiba, Japan, Domain Decomposition Press, Bergen, 2001, pp. 15-28

[6] M.J. Gander; F. Magoulès; F. Nataf Optimized Schwarz methods without overlap for the Helmholtz equation, SIAM J. Sci. Statist. Comput., Volume 24 (2002) no. 1, pp. 38-60

[7] M. Garbey; D. Tromeur-Dervout On some Aitken like acceleration of the Schwarz method, Int. J. Numer. Methods Fluids, Volume 40 (2002) no. 12, pp. 1493-1513

[8] L. Gerardo Giorda, F. Nataf, Optimized Schwarz methods for unsymmetric layered problems with strongly discontinuous and anisotropic coefficients, RR 561, CMAP, 2004

[9] C. Japhet; F. Nataf; F. Rogier The optimized order 2 method: application to convection–diffusion problems, Future Generation Computer Systems FUTURE, Volume 18 (2001)

[10] P.-L. Lions On the Schwarz alternating method. III: A variant for nonoverlapping subdomains (T. Chan; R. Glowinski; J. Périaux; O. Widlund, eds.), Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, held in Houston, TX, March 20–22, 1989, SIAM, Philadelphia, PA, 1990

[11] Y. Maday, F. Magoulès, Multilevel optimized Schwarz methods without overlap for highly heterogeneous media, RR-05015, Université Pierre & Marie Curie, Laboratoire Jacques-Louis Lions, 2005

[12] F. Magoulès, I. Harari (Eds.), Absorbing boundary conditions, Comput. Methods Appl. Mech. Engrg., 2005, in press

[13] F. Magoulès; P. Iványi; B.H.V. Topping Non-overlapping Schwarz methods with optimized transmission conditions for the Helmholtz equation, Comput. Methods Appl. Mech. Engrg., Volume 193 (2004) no. 45–47, pp. 4797-4818

[14] F. Nataf, F. Rogier, E. de Sturler, Optimal interface conditions for domain decomposition methods, RR 301, CMAP, 1994

[15] H.A. Schwarz, Über einen Grenzübergang durch alternierendes Verfahren, Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich 15 (May 1870) 272–286

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