Domain Decomposition Methods via Boundary Integral Equations
Date
2000-12-21
Journal Title
Journal ISSN
Volume Title
Publisher
Department of Mathematical Sciences
Abstract
Domain decomposition methods are designed to deal with coupled or transmission
problems for partial differential equations. Since the original boundary value problem is replaced by local problems in substructures, domain decomposition methods are well suited for both parallelization and coupling of different discretization
schemes. In general, the coupled problem is reduced to the Schur complement equation on the skeleton of the domain decomposition. Boundary integral equations are
used to describe the local Steklov-Poincare operators which are basic for the local
Dirichlet-Neumann maps. Using different representations of the Steklov-Poincare
operators we formulate and analyze various boundary element methods employed
in local discretization schemes. We give sufficient conditions for the global stability
and derive corresponding a priori error estimates. For the solution of the resulting
linear systems we describe appropriate iterative solution strategies using both local
and global preconditioning techniques.
Description
Keywords
domain decomposition, boundary integral equations, boundary element methods, preconditioning techniques