Parallel implementation of a Schwarz Domain Decomposition Algorithm

. We describe and compare some recent domain decomposition algorithms of Schwarz type with respect to parallel performance. A new, robust domain decomposition algorithm -- Additive Average Schwarz is compared with a classical overlapping Schwarz code. Complexity estimates are given in both two and three dimensions and actual implementations are compared on a Paragon machine as well as on a cluster of modern workstations. 1 Introduction This paper is concerned with parallel algorithms for the numerical solution of equations of the form: Find u 2 V (\Omega ) such that N X i=1 Z \Omega i ae i ru \Delta rv dx = Z \Omega fv dx 8v 2 V (\Omega ); (1) in a space V (\Omega ) ae H 1 (\Omega ). Here ae i are positive constants and ¯\Omega = [ N i=1 ¯\Omega i . This problem is important in many fields of application, an example being the study of flow in porous media [2]. Domain decomposition algorithms have received much attention in the last ten years due to their potent..