Domain Decomposition Methods for Partial Differential Equations On Parallel Computers

In this paper we review several methods for solving large sparse linear systems arising from discretization of elliptic partial differential equations on parallel com puters. The main idea is to use domain decomposition to introduce some parallelism. We describe techniques such as the Schwarz algorithm and the block incomplete factorization method, showing with examples the effi ciency of these domain decomposition techniques when the number of subdomains is increased.