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-Poincare operators, for a class of linear ex terior boundary value problems arising in potential theory and heat co nductivity. 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. T his domain is decomposed into a finite number of annular subregions, a nd the Dirichlet data on the interfaces is introduced as the unknown o f the associated Steklov-Poincare problem. This problem is solved with the Richardson method by introducing a Dirichlet-Robin-type precondit ioner, which yields an iteration-by-subdomains algorithm well suited f or parallel computations. The corresponding analysis for the finite el ement approximations and some numerical experiments are also provided. (C) 1998 Elsevier Science Ltd. All rights reserved.