Abstract
In this dissertation, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The goal of this study was to investigate the similarities of spectral domain analysis and the FMM formulation. The benefit of the spectral domain analysis such as transforming the convolutional form of the Green's function to multiplication form are incorporated in the SD-FMM method. The study focuses on the application of SD-FMM to one-, two- and three-dimensional electric field integral equation (EFIE). The cases of perfectly conducting (PEC) strips, circular and square perfectly conducting cylinders are numerically analyzed. For three-dimensional cases, a perfectly conductor sphere, square flat plate, and circular disk are also analyzed. The results from the SD-FMM method are compared with the results from the conventional FMM and the direct application of Method of Moments (MoM). All the results compared well with results from the direct application of MoM.