New Techniques and Applications for Computational Electromagnetics

摘要

Several different aspects of numerical methods for electromagnetic scattering are considered. The interior source method is one major focus of the research. It is shown how the scattered field can be extended to the interior of a scatterer with a view to determining the locations of singular points of the extended field. These results are of immediate use to synthesize the scattered field. The interior source method has been applied to solving a number of scattering problems, mostly but not exclusively from smooth bodies. Spectral convergence of the approximations has been demonstrated and this permits far fewer unknowns to be used in the computation than would be the case with methods in which the sources are distributed on the boundary of the scattering body. A second topic of research concerns the finite difference time domain technique (FDTD). For this method a new approach to handling complex geometrical situations has been developed. This approach uses at least squares technique in conjunction with a novel but simple form of description of the boundary of the body. It converges at or close to a rate of second order in the spatial variables in contrast to a number of other algorithms designed to solve the same problem.