PARALLEL SCHWARZ ALGORITHM WITH UNDER-RELAXED PSEUDO-BOUNDARY CONDITIONS IN DOMAIN DECOMPOSITION METHOD

Abstract

The parallel Schwarz algorithm for solving partial differential equations in a two-subdomain case and its convergence feature are summarized. Under-relaxation in pseudo-boundary conditions as an acceleration scheme is introduced and its convergence is analyzed in this paper. In addition, several iteration strategies which exploit the attractive feature of the under-relaxation scheme in pseudo-boundary conditions are investigated via numerical experiments. The results show that superlinear speedup can easily be obtained if adequate iteration strategies are adopted.