Efficient Methods for Solving Electromagnetic Wave Scattering From Dielectric Objects Using the Method of Moments With the Interpolation Fast Fourier Transform Method

Abstract

The method of moments discretizes an integral equation and produces a matrix. The computational complexity of using direct inversion is proportional to O(N<sup>3</sup>) and O(N<sup>2</sup>) for the number of operation and memory requirements, respectively, where N is the number of unknowns in a problem. Hence, iterative methods are used when the computational complexity is proportional to O(N<sup>2</sup>). If the integral is discretized on a uniform grid, the resultant matrix is Toeplitz and the matrix-vector product can only be performed using the fast Fourier transform (FFT) method with O(N log N) operations and memory requirements of O(N). Unfortunately, for realistic problems, this is rarely the case since the irregularity of realistic shapes leads to a non-uniform grid; therefore, the FFT method is not applicable. In this study, cubic spline interpolation was used successfully in two different ways to obtain a Toeplitz matrix if the dielectric object was homogenous or a matrix containing Toeplitz submatrices if the dielectric object was inhomogeneous. The results obtained when applying these methods to solve electromagnetic scattering from two- and three-dimensional dielectric objects showed that both approaches are accurate and efficient.