Analysis of patch substructuring methods

• Autorzy: Martin J. Gander , Laurence Halpern , Frédéric Magoulès , Francois-Xavier Roux
• Języki publikacji: EN

Abstrakty

EN

Patch substructuring methods are non-overlapping domain decomposition methods like classical substructuring methods, but they use information from geometric patches reaching into neighboring subdomains condensated, on the interfaces to enhance the performance of the method, while keeping it non-overlapping. These methods are very convenient to use in practice, but their convergence properties have not been studied yet. We analyze geometric patch substructuring methods for the special case of one patch per interface. We show that this method is equivalent to an overlapping Schwarz method using Neumann transmission conditions. This equivalence is obtained by first studying a new, algebraic patch method, which is equivalent to the classical Schwarz method with Dirichlet transmission conditions and an overlap corresponding to the size of the patches. Our results motivate a new method, the Robin patch method, which is a linear combination of the algebraic and the geometric one, and can be interpreted as an optimized Schwarz method with Robin transmission conditions. This new method has a significantly faster convergencerate than both the algebraic and the geometric one. We complement our results by numerical experiments.

Słowa kluczowe

EN

patch substructuring methods; Schur complement methods; Schwarz domain decomposition methods; optimized Schwarz methods

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2007
• Tom: 17
• Numer: 3
• Strony: 395-402

Daty

wydano

2007

Twórcy

autor

Martin J. Gander

• Section de Mathématiques, Université de Genève, 1211 Genève, Switzerland

autor

Laurence Halpern

• LAGA, Institut Galilée, Université Paris 13, 93430 Villetaneuse, France

autor

Frédéric Magoulès

• Applied Mathematics and Systems Laboratory, Ecole Centrale Paris, 92295 Châtenay-Malabry Cedex, France

autor

Francois-Xavier Roux

• High Performance Computing Research Unit ONERA, 92322 Chatillon, France

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