A Nonoverlapping Domain Decomposition Method 3

A parallel iterative nonoverlapping domain decomposition method is proposed and analyzed for elliptic problems. Each iteration in this method contains two steps. In the rst 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 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 diierential level by Hilbert space techniques. Numerical results are provided to connrm the convergence theory.