Parallel implementation of the Schwarz method for the Poisson problem

Abstract

We discuss the additive Schwarz method for solving the Poisson problem. Additive Schwarz method is one of well known overlapping domain decomposition methods which effectively solve elliptic partial differential equations. The performance of this method dependent upon the overlap size and the number of subdomains. In this thesis, we study how these factors affects the performance. For each subdomain, the additive Schwarz method needs to solve the linear system. As a local system solver, we consider the Gaussian Elimination and the Conjugate Gradient method. Then we compare their efficiencies in the Schwarz algorithm. We finally use the additive Schwarz preconditioner with the overlap size and the number of subdomains determined by the numerical tests. Then we observe the effect of the additive Schwarz preconditioner.