Domain Decomposition Method Of Infinite Domain

In this paper, through the idea of domain decomposition method and the theory of natural boundary reduction, we study overlapping domain decomposition method and non-overlapping domain decomposition method for elliptic boundary value problems in an infinite domain. For the non-overlapping DDM, the author gives a practice of Dirichlet-Neumann alternating algorithm, which the direct promotion of two sub-domain of the D-N alternating method. Discrete D-N algorithm is given. The convergence of algorithm is given and it is equivalent to the Richardson iterative algorithm. Our method is performance for the science and engineering problems which reduces the scale of the calculation. For overlapping domain decomposition method, the author puts forward a structure of parallel Schwarz alternating algorithm. The convergence of this algorithm is given and the convergence rate of the algorithm for an exterior circular domain is also analyzed. It is explained that the parallel algorithm is higher than the general domain decomposition method in the efficiency of calculation, and our method is performance for the large-scale problem.