Fast method for solving integral equations of electromagnetic wave scattering from perfect conductor three-dimensional objects using Fourier series

In this paper, an easy method is proposed to reduce the computational complexity of matrix-vector multiplication that is required in solving integral equations using method of moments. This method approximates the Green's function using a Fourier series. It has the advantage that its formulation separates the observation point from the source point effortlessly and regardless of the Green's function. Since the fast multipole method uses this idea, the two methods are discussed and compared theoretically and numerically by solving the electromagnetic wave scattering from perfect conductor of three-dimensional basic canonical shape (sphere). The results showed that the proposed method is accurate, and for large number of unknowns in the problem, it has a computational complexity less than the method of moments and over the conventional fast multipole method. Hence, the generality and simplicity of this method compare with the conventional fast multipole method and the efficiency compare with the method of moments, which will be achieved.