Efficient Method for Solving TM-Polarized Plane Wave Scattering from Two-Dimensional Perfect Conductor Surfaces Using Fourier Series Approximation of the Green’s Function

Abstract

The method of moments generates a matrix which is usually solved using iterative methods due to the high computational complexity of a direct inversion. The cost of matrix-vector multiplications and memory requirement at each iteration step is proportional to O(N2), where N is the number of unknowns in the problem. To reduce the computational complexity, the Green’s function is approximated using Fourier series. This will allow to separate the source points from the observation points. Hence, aggregate all source points and then multiply it with each observation point with a small adjustment in the aggregation term. The proposed method is tested by solving electromagnetic wave scattering from perfect conductor two-dimensional basic canonical shape, i.e., circular cylinder. The results showed that the proposed method is accurate and for large N it has a computational complexity less than the direct matrix-vector multiplication.