Title: Introduction to Domain Decomposition Methods for CFD

Speaker: Professor David Keyes
Columbia University, Department of Applied Physics and Applied Mathematics

Iterative solvers based on domain decomposition originated as means of extending the generality of direct solvers limited by structure or available memory by "divide-and-conquer" and evolved rapidly in the last two decades to general purpose algebraic techniques suited for scalable computer architectures.  In this talk, we briefly survey some themes in domain decomposed iterative methods for linear problems: algorithms of Schwarz type, convergence results, and scalability estimates. We argue the advantages of domain decomposition over other types of parallel algorithms for PDEs on massively parallel machines. We illustrate with recent Gordon Bell prizes based on domain decomposition and mention available software. For fluid dynamical applications, we discuss two strategies for nonlinear problems, one being simply a domain-decomposed extension of Newton's method with Schwarz iteration on the linear subproblems and the other being a fundamentally nonlinear Schwarz iteration.