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Improved interface conditions for \(2 D\) domain decomposition with corners: numerical applications. (English) Zbl 1203.65274
Summary: 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 by the authors [Calcolo 45, No. 2, 111–147 (2008; Zbl 1173.65364)], the numerical experiments presented in this article confirm the optimality properties of the new interface conditions.

MSC:
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
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[1] Chan, T.F., Mathew, T.P.: Domain decomposition algorithms. In: Acta Numerica 1994, pp. 61–143. Cambridge Univ. Press, Cambridge (1994) · Zbl 0809.65112
[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) · Zbl 1173.65364
[3] FreeFem++: http://www.freefem.org
[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)
[5] Nataf, F., Nier, F.: Convergence rate of some domain decomposition methods for overlapping and nonoverlapping subdomains. Numer. Math 75, 357–377 (1997) · Zbl 0873.65108 · doi:10.1007/s002110050243
[6] Nier, F.: Remarques sur les algorithmes de décomposition de domaines. In: Séminaire EDP-Ecole Polytechnique 1998-99, Exp. No IX, 26 · Zbl 1058.65514
[7] Quarteroni, A., Valli, A.: Domain Decomposition Methods for Partial Differential Equations. Oxford Science Publications, Oxford (1999) · Zbl 0931.65118
[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) · Zbl 0377.65058
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