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. © 1998 Elsevier Science Ltd. All rights reserved.
Gatica, G. N., Hernandez, E. C., & Mellado, M. E. (1998). A domain decomposition method for linear exterior boundary value problems. Applied Mathematics Letters, 1-9. https://doi.org/10.1016/S0893-9659(98)00093-7