Domain Decomposition Methods for Partial Differential Equations

Abstract

Domain decomposition methods are iterative methods for the solution of linear or nonlinear systems that use explicit information about the geometry, discretization, and/or partial differential equations that underlie the discrete systems. Considerable research in domain decomposition methods for partial differential equations has been carried out in the past dozen years. Recently, these techniques have begun to be applied to “real-world” engineering problems. This chapter summarizes basic ideas of domain decomposition methods. Though no particular applications are discussed, references are furnished to several recent uses of domain decomposition.