In this paper, based on the natural boundary reduction suggested by Feng and Yu, an overlapping domain decomposition method with its discretization is discussed. This method is very effective especially for problems o...In this paper, based on the natural boundary reduction suggested by Feng and Yu, an overlapping domain decomposition method with its discretization is discussed. This method is very effective especially for problems over unbounded domains. The geometric convergency of both continuous and discrete problems is proved. The theoretical results as well as the numerical examples show that the convergence rate of this discrete Schwarz iteration is independent of the finite element mesh size, but dependent on the frequency of the exact solution and the overlapping degree of the subdomains.展开更多
文摘In this paper, based on the natural boundary reduction suggested by Feng and Yu, an overlapping domain decomposition method with its discretization is discussed. This method is very effective especially for problems over unbounded domains. The geometric convergency of both continuous and discrete problems is proved. The theoretical results as well as the numerical examples show that the convergence rate of this discrete Schwarz iteration is independent of the finite element mesh size, but dependent on the frequency of the exact solution and the overlapping degree of the subdomains.
