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Journal of Scientific Computing

, Volume 38, Issue 2, pp 207–228 | Cite as

Improved Interface Conditions for 2D Domain Decomposition with Corners: Numerical Applications

  • Chokri Chniti
  • Frédéric NatafEmail author
  • Francis Nier
Article

Abstract

This article deals with a local improvement of domain decomposition methods for 2-dimensional elliptic problems for which either the geometry or the domain decomposition presents conical singularities. After explaining the main results of the theoretical analysis carried out in Chniti et al. (Calcolo 45, 2008), the numerical experiments presented in this article confirm the optimality properties of the new interface conditions.

Keywords

Domain decomposition method Corner singularity Kondratiev theory 

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References

  1. 1.
    Chan, T.F., Mathew, T.P.: Domain decomposition algorithms. In: Acta Numerica 1994, pp. 61–143. Cambridge Univ. Press, Cambridge (1994) Google Scholar
  2. 2.
    Chniti, C., Nataf, F., Nier, F.: Improved interface condition for 2D domain decomposition with corner: a theoretical determination. Prépublication IRMAR 06-02, Calcolo 45 (2008) Google Scholar
  3. 3.
  4. 4.
    Japhet, C., Nataf, F.: The best interface Conditions for domain decomposition methods: Absorbing boundary conditions. In: Absorbing Boundaries and Layers, Domain Decomposition Methods, pp. 348–373. Nova Sci. Publ., New York (2001) Google Scholar
  5. 5.
    Nataf, F., Nier, F.: Convergence rate of some domain decomposition methods for overlapping and nonoverlapping subdomains. Numer. Math 75, 357–377 (1997) zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Nier, F.: Remarques sur les algorithmes de décomposition de domaines. In: Séminaire EDP-Ecole Polytechnique 1998-99, Exp. No IX, 26 Google Scholar
  7. 7.
    Quarteroni, A., Valli, A.: Domain Decomposition Methods for Partial Differential Equations. Oxford Science Publications, Oxford (1999) zbMATHGoogle Scholar
  8. 8.
    Raugel, G.: Résolution numérique par une méthode d’éléments finis du problème de Dirichlet pour le laplacien dans un polygone. C. R. Acad. Sci. Paris Ser. A 286, 791–794 (1978) zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.CMAP, UMR CNRS 7641, Ecole PolytechniquePalaiseau CedexFrance
  2. 2.Laboratoire Jacques-Louis LionsUMR CNRS 7598Paris, Cedex 05France
  3. 3.IRMARUMR CNRS 6625, Université de Rennes IRennes CedexFrance

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