A domain decomposition method for linear exterior boundary value problems

In this paper, we present a domain decomposition method, based on the general theory of Steklov-Poincaré operators, for a class of linear exterior boundary value problems arising in potential theory and heat conductivity. We first use a Dirichlet-to-Neumann mapping, derived from boundary integral eq...

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Veröffentlicht in:Applied mathematics letters Jg. 11; H. 6; S. 1 - 9
Hauptverfasser: Gatica, G.N., Hernandez, E.C., Mellado, M.E.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.11.1998
Schlagworte:
Dirichlet-Robin sweep
Dirichlet-to-Neumann mapping
Iteration by subdomains
Steklov-Poincaré operator
Steklov-Poincaré operator
Dirichlet-Robin sweep
Iteration by subdomains
Dirichlet-to-Neumann mapping
ISSN:0893-9659, 1873-5452
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Zusammenfassung:In this paper, we present a domain decomposition method, based on the general theory of Steklov-Poincaré operators, for a class of linear exterior boundary value problems arising in potential theory and heat conductivity. We first use a Dirichlet-to-Neumann mapping, derived from boundary integral equation methods, to transform the exterior problem into an equivalent mixed boundary value problem on a bounded domain. This domain is decomposed into a finite number of annular subregions, and the Dirichlet data on the interfaces is introduced as the unknown of the associated Steklov-Poincaré problem. This problem is solved with the Richardson method by introducing a Dirichlet-Robin-type preconditioner, which yields an iteration-by-subdomains algorithm well suited for parallel computations. The corresponding analysis for the finite element approximations and some numerical experiments are also provided.
ISSN:0893-9659
1873-5452
DOI:10.1016/S0893-9659(98)00093-7