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A domain decomposition method for linear exterior boundary value problems

✍ Scribed by G.N. Gatica; E.C. Hernandez; M.E. Mellado

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
697 KB
Volume
11
Category
Article
ISSN
0893-9659

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✦ Synopsis

this paper, we present a domain decomposition method, based on the general theory of Steklov-Poincare 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 asso ciated Steklov-Poincare 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.

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