A fast IE-FFT algorithm for solving PEC scattering problems

This paper presents a novel fast integral equation method, termed IE-FFT, for solving large electromagnetic scattering problems. Similar to other fast integral equation methods, the IE-FFT algorithm starts by partitioning the basis functions into multilevel clustering groups. Subsequently, the entire impedance matrix is decomposed into two parts: one for the self and/or near field couplings, and one for well-separated group couplings. The IE-FFT algorithm employs two discretizations one is for the unknown current on an unstructured triangular mesh, and the other is a uniform Cartesian grid for interpolating the Green's function. By interpolating the Green's function on a regular Cartesian grid, the couplings between two well-separated groups can be computed using the fast Fourier transform (FFT). Consequently, the IE-FFT algorithm does not require the knowledge of addition theorem. It simply utilizes the Toeplitz property of the coefficient matrix and is therefore applicable to both static and wave propagation problems.