A Domain Decomposition Method For Electromagnetic Problems On Unbounded Domains

In this thesis, we investigate the numerical method for the electromagnetic wave by the theory of the natural boundary reduction and the key idea of the domain decomposition algorithm.In the first chapter, by the principle of the natural boundary reduction, the Schwarz alternating algorithm based on the natural boundary reduction for the electromagnetic scattering of transverse magnetic field in plane with a cavity is presented. The geometric convergence in the sense of energy norm is proved by projection theory. Finally, some numerical examples are given to demonstrate the feasibility and effectiveness of the algorithm.In the second chapter, by the principle of the natural boundary reduction, the Dirichlet-Neumann alternating algorithm (D-N alternating algorithm) for the electromagnetic scattering of transverse electric field in plane with a cavity is presented. The convergence of the algorithm is analyzed. It is proved that the convergence rate is independent of the finite mesh size, the D-N alternating algorithm is equivalent to preconditioned Richardson iteration method. Finally, some numerical examples are given to test the feasibility and effectiveness of the algorithm.