An Optimal Two-Level Overlapping Domain Decomposition Method for Elliptic Problems in Two and Three Dimensions

We consider the solution of linear systems of algebraic equations that arise from elliptic nite element problems We study a two level overlapping domain decomposition method that can be viewed as a combination of the additive and multiplicative Schwarz methods This method combines the advantages of the two methods It converges faster than the additive Schwarz algorithm and is more parallelizable than the multiplicative Schwarz algorithm and works for general not necessarily selfadjoint linear second order elliptic equations We use the GMRES method to solve the resulting preconditioned linear system of equations and we show that the algorithm is optimal in the sense that the rate of convergence is independent of the mesh size and the number of subregions in both R and R A numerical comparison with the additive and multiplicative Schwarz preconditioned GMRES is reported