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In this paper, 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 is to investigate the similarities and differences between the spectral domain analysis and conventional FMM formulation. The benefit of the spectral domain analysis such as transforming the convolutional form of the Green’s function to a multiplicative form is 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 electric conducting (PEC) strips, circular perfectly conducting cylinders, and perfectly conductor spheres are 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). The SD-FMM results agree well with results from the direct application of MoM.

SPECTRAL DOMAIN FAST MULTIPOLE METHOD FOR SOLVING INTEGRAL EQUATIONS OF ELECTROMAGNETIC WAVE SCATTERING