IMPROVEMENT OF THE RATE OF CONVERGENCE OF THE CONJUGATE GRADIENT FAST FOURIER TRANSFORM METHOD FOR ANALYZING PLANAR FREQUENCY SELECTIVE SURFACES

Abstract

In this paper two methods are shown to improve the rate of convergence of the Conju- gate Gradient Fast Fourier Transform (CG-FFT) method for analyzing planar frequency selective surfaces (FSS) with finite conductivity and with arbitrary angles of incidence. After formulating the physical model an operator equation is written for the induced surface current which is first solved by the CG-FFT method. Here the norm and inner product are defined in detail. Then the problem of the preconditioning is discussed and a new procedure called Biconjugate Gradient fast Fourier transform (BiCG-FFT) method is developed. It is demonstrated that this procedure requires a smaller number of iterations than the original or the preconditioned CG-FFT method. At the end of the paper results of the analysis of an infinite rectangular grid ob- tained by the different methods are given and compared according to precision and rate of convergence.