Investigation of Schwarz Domain Decomposition Using Accurate and InaccurateSolution of Subdomains

摘要

For the solution of practical complex problems in arbitrarily shaped domains,simple Schwarz domain decomposition methods with minimal overlap are used. Krylov subspace methods, such as the GMRES method, can be used to obtain significant acceleration of convergence. When accurate solution of subdomains is presupposed, this acceleration procedure can be quite efficient but the amount of time spent in solving subdomain problems may be prohibiting. To reduce computing time, inaccurate solution of subdomains is considered. This requires a different, GCR based, acceleration technqiue. Experiments show that computing time for a multi-domain problem can be reduced to that of single domain solution with the same total number of unknowns. For this purpose, the multiplicative domain decomposition algorithm should be used. This is an important practical observation, since this makes efficient domain decomposition available for complex problems, for which parallel implementation is not readily available, possible or feasible. The prospects for parallel implementation are also investigated.