Domain Decomposition Method For Some 2-D And 3-D Problems

In this paper, through the theory of natural boundary reduction, we study the domain decomposition methods for some 2-D and 3-D problems. It contains overlapping domain decomposition method outside fan-shaped domain and non-overlapping domain decomposition method over unbounded half plane. For the overlapping DDM (Schwarz alternating algorithm), the author mainly studys on the irregular region outside fan-shaped domain, and the convergence of this algorithm is given. We also deal this method with FEM. This algorithm can solve some large-scale problems in effect. Explaining the non-overlapping domain decomposition method for 2-D simplely. For the non-overlapping DDM(D-N alternating algorithm), the author promotes 2-D problem to the 3-D problem, resolving 3-D Dirichlet outside value problem over unbounded half plane. The method is equivalent to the Richardson iterative algorithm, the convergence of this algorithm is also analyzed and the convergence rate of this algorithm is unrelated to the Mesh parameter h. The value range of relaxation factor is also given.the scale of the calculation is reduced, and the algorithm therefore can convenient be used in practice.