On the Domain Decomposition Method Preconditioning of Surface Integral Equation Formulations Solved by GMRES

In this communication, the performance of the generalized minimum residual method (GMRES) preconditioned by a domain decomposition method (DDM) scheme embedded in a surface integral equation (SIE) formulation is studied. In realistic large multiscale problems, the individual subdomain solutions, which in a DDM scheme acts as the preconditioners, have to be obtained by the Krylov subspace iterative processes with a decisive influence on the outcome of the overall iterative process that deals with subdomains' mutual couplings. The convergence and accuracy of the global solution, as well as the degree of correlation between them, are studied for the left-, right-, and flexible-right-preconditioned GMRES to draw conclusions which maximize the efficiency in the application of the SIE-DDM implementation to challenging problems.