(Demnin Decomposition Methods For An Exerior2-D Schr(?)dinger Equations)

In this thesis, by means of the theory of the natural boundary reduction and the key idea of the domain decomposition algorithm, we investigate the domain decomposition methods for an exterior2-D Schrodinger equation.In chapter1, firstly, by means of the Newmark method, the derivative in equation is discretized, semi-discrete form is given, and the exterior Helmholtz problem at each time-step is obtained by an appropriate transformation. Sec-ondly, the Poisson integral formula and the natural integral equation are ob-tained by the principle of the natural boundary reduction. Thirdly, the Dirichlet-Neumann alternating algorithm (D-N alternating algorithm) based on the natural boundary reduction is presented. The convergence of the algorithm is analyzed. It is proved that the convergence rate is independent of the finite mesh size, and the D-N alternating algorithm is equivalent to the preconditioned Richardson it-eration method. Finally, some numerical examples are given to test the feasibility and effectiveness of the algorithm.In chapter2, by the principle of the natural boundary reduction, the Schwarz alternating algorithm based on the natural boundary reduction is presented. The geometric convergence in the sense of energy norm is proved by projection the-ory. Finally, some numerical examples are given to demonstrate the feasibility and effectiveness of the algorithm.