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Improved interface conditions for a non-overlapping domain decomposition of a nonconvex polygonal domain. (English) Zbl 1096.65124
Summary: We propose a local improvement of domain decomposition methods which fits with the singularities occurring in the solutions of elliptic equations in polygonal domains. This short presentation focuses on a model elliptic problem with the decomposition of a nonconvex polygonal domain into convex polygonal subdomains. After explaining the strategy and the theoretical design of adapted interface conditions at the corner, we present numerical experiments which show that these new interface conditions satisfy some optimality properties.

MSC:
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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[1] Chniti, C.; Nataf, F.; Nier, F., Improved interface condition for 2D domain decomposition with corner: a theoretical determination · Zbl 1173.65364
[2] Japhet, C.; Nataf, F., The best interface conditions for domain decomposition methods: absorbing boundary conditions, (), 348-373
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[4] F. Nier, Remarques sur les algorithmes de décomposition de domaines, in : Séminaire EDP de l’Ecole Polytechnique (1998-1999), Exposé numéro IX
[5] Quarteroni, A.; Valli, A., Domain decomposition methods for partial differential equations, (1999), Oxford Science Publications xxx · Zbl 0931.65118
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