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Optimized Schwarz methods for a diffusion problem with discontinuous coefficient

Gander, Martin ; Dubois, Olivier

In: Numerical Algorithms, 2015, vol. 69, no. 1, p. 109-144

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    Titre
    • Optimized Schwarz methods for a diffusion problem with discontinuous coefficient
    Auteur
    • Gander, Martin. Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, C.P. 64 1211, Genève 4, Suisse
    • Dubois, Olivier. Department of Mathematics, John Abbott College, 21275 Lakeshore Road, Sainte-Anne-de-Bellevue, H9X 3L9, Québec, Canada
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Numerical Algorithms, 2015, vol. 69, no. 1, p. 109-144. Springer US; http://www.springer-ny.com
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:331706
    Summary
    We study non-overlapping Schwarz methods for solving a steady-state diffusion problem in heterogeneous media. Various optimized transmission conditions are determined by solving the corresponding min-max problems; we consider different choices of Robin conditions and second order conditions. To compare the resulting methods, we analyze the convergence in two separate asymptotic regimes: when the mesh size is small, and when the jump in the coefficient is large. It is shown that optimized two-sided Robin transmission conditions are very effective in both regimes; in particular they give mesh independent convergence. Numerical experiments are presented to illustrate and confirm the theoretical results.