Electromagnetic scattering by numerical methods applicable for large structures

Abstract

The objective of this research is to develop numerical methods for general and efficient solutions to the linear systems obtained using the integral equations arising from electromagnetic scattering problems involving electrically large structures. In the process, the prior art in this area is reviewed. Then, the integral equations and their solutions by the method of moments (MoM) are derived. The progressive numerical method (PNM) and the projection iterative method (PIM) are analysed, including formulations, operation counts, stopping criteria, and their connection. In practice, the PNM is successful in calculation of two-dimensional scattering problems. The iterative PNM and a special case of the PNM, the modified spatial decomposition technique (SDT), are applied to the problems and compared with the PNM. Examples show that the PNM can depress internal resonances. The PIM is implemented in the two-dimensional TE case and convergent solutions are obtained. In order to overcome the difficulties with three-dimensional scattering problems, the PIM is implemented to solve the matrix equation obtained by MoM. Convergent results are observed in all examples being calculated for two- and three-dimensional objects. The PIM's iteration process can be accelerated by appropriate relaxation factors. The dependence of optimum relaxation factors on various parameters are investigated. Approximate results of large objects are obtained by the PIM with much less computation effort than the direct method. By allowing certain smaller elements in a coefficient matrix to be zero, the PIM can be further sped up, while still getting good far field results. This technique was found to be object dependent, providing better results for spheres than other objects.