A parallel iterative nonoverlapping domain decomposition procedure for elliptic problems

Abstract

A parallel iterative nonoverlapping domain decomposition method is proposed and analyzed for elliptic problems. Each iteration in this method contains two steps. In the first step, at the interface of two subdomains, one subdomain problem requires that Dirichlet data be passed to it from the previous iteration level, while the other subdomain problem requires that Neumann data be passed to it. In the second step, we interchange the types of data passing at the interface of the two subdomains. This domain decomposition method is suitable for parallel processing with coarse granularity. Convergence analysis is demonstrated at the differential level by Hilbert space techniques. Numerical results are provided to confirm the convergence theory.