A Dirichlet-Nenmann Alternating Algorithm For Electromagnetic Scattering Problems On Half-unbounded Domains

In this thesis, we investigate the non-overlapping domain decomposition method (D-N alternating algorithm) for some electromagnetic scattering prob-lems in the upper half of plane.Electromagnetic scattering problems in R2include transverse magnetic field and transverse electric field. For each case, the governing equation is first dis-cretized in time by the Newmark method, leading to a time-stepping scheme, where an exterior Helmholtz problem has to be solved in each time step. An arti-ficial boundary ΓR is introduced, a boundary condition on the artificial boundary condition ΓR is obtained by the principle of the natural boundary reduction, the original problem is reduced a computational problem in a bounded domain, and a corresponding variational problem is given. Secondly, the numerical solution is obtained by the D-N alternating method, the convergence of the algorithm is an-alyzed. The convergence rate is independent of the finite element mesh size. And it is proved that the D-N alternating algorithm is equivalent to preconditioned Richardson iteration method. Finally, some numerical examples are presented to illustrate the feasibility of the method.