Partitioned-GMRES in Domain Decomposition with Approximate Subdomain Solution

Solution of large linear systems encountered in computational fluid dynamics often leads to some form of domain decomposition, especially when it is desired to use parallel machines. In this paper P-GMRES, a partitioned modification of GMRES, is applied to such problems. It is shown that P-GMRES converges faster than GMRES if the subdomains are solved exactly, and that P-GMRES requires less communication in the computation of the inner products. Also, approximate solutions for the subdomains by an inner preconditioned GMRES iteration are considered, in combination with a restarted version of P-GMRES. It turns out that rather crude tolerances are allowed, and that a good strategy is to vary the tolerance for the subdomains in the course of the outer iteration.This revised version was published online in October 2005 with corrections to the Cover Date.