Efficient method of moments for compact large planar scatterers in homogeneous medium

Abstract

An efficient method for analyzing large planar scatterers in a homogeneous medium is implemented. A space domain method of moment (MoM) approach has been employed since the corresponding spatial Green's functions are simple and available in closed form. In order to minimize the singular behavior attached to the Green's functions, the electric field is expressed in terms of vector and scalar potentials, thus leading to a mixed potential integral equation (MPIE) system. The mutual impedance coefficients to be determined are four-fold integrals and contribute to much of the computation cost of the matrix filling. They can be reduced to two-fold by transferring the del operator (/spl nabla/) from the Green's functions kernel to the testing functions and substituting analytical expressions for the resulting cross correlations between the expansion and testing functions. The remaining two-fold integrals are evaluated numerically using a quadrature method which minimizes the number of functional evaluations. The singular integrals are evaluated efficiently by transforming them to polar coordinates. The selection of a uniform grid further introduces some symmetries. These symmetries are exploited to reduce the computational complexity to less than one fifth of the original. Hence, we can save the computer memory usage by mapping the calculated coefficients in an innovative way rather than storing them explicitly. The resulting equation system is solved by applying an iterative matrix solving algorithm called the conjugate gradient (CG). The matrix multiplications encountered in the implementation of CG algorithm are efficiently performed using the fast Fourier transform (FFT) thus reducing the matrix solution time significantly. The present approach is applied for analyzing large planar scatterers and the results are presented.