Domain Decomposition Methodsfor Partial Differential

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 diierential equation (PDE) that gave rise to the (non)linear system. A large amount of research in domain decomposition methods for partial diierential equations has been carried out in the past dozen years. Recently, these techniques have begun to be applied to \real-world" engineering problems. This summary introduces the basic ideas in domain decomposition methods for PDEs. Though no particular applications are discussed, references to several recent uses of domain decomposition are given.