An Overview Of Optimized Schwarz Methods

Optimized Schwarz method is a new class of domain decomposition method based on classical Schwarz method and it has a good performance in both the convergence and the parallel computing. This thesis is an overview about the optimized Schwarz method. We first give the history and the current research about the optimized Schwarz method, and point out the current research problems and the advantages of the method. Next, we consider the following model in two dimensional space and discuss the design of the method, the optimization of the transmission and the convergence. At last, we take the following Maxwell's equation curlas an model to interpret the applications of the optimized Schwarz method in physical problems. The comparison and analysis of the convergence factors in both the optimized and the classical Schwarz method show that the optimized Schwarz method is more efficiency in scientific computing.