Domain Decomposition Algorithm Of Elliptic Boundary Value Problems In Infinite Concave Angle

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, which is named Dirichlet-Neumann alternating algorithm, we prove the convergence of the algorithm, and it is equivalent to the Richardson iterative algorithm. Discrete D-N algorithm and some numerical examples are given. For overlapping domain decomposition method, which is named Schwarz alternating algorithm, we prove the geometric convergence for continuous algorithm in the sense of energy norm by means of projection theory, and the convergence rate of the algorithm. Some numerical examples are given. Numerical examples illustrate feasibility and efficiency of our methods.