Adaptive Integral Method (AIM) Combined with the SSOR Preconditioned CG Algorithm for Planar Structures Analysis

Abstract

In this paper, the adaptive integral method (AIM) is used to analyze the large-scale planar structures. To discretize the integrate equations by using of method of moment (MoM) with Rao-Wilton-Glisson (RWG) basis functions can model arbitrarily shape planar structures but usually leads to a fully populated matrix. AIM could map these basis functions onto a rectangular grid then the Toeplitz property of the Green's function would be utilized, which enables the calculation of matrix-vector multiplication by use of the fast Fourier transform (FFT). This algorithm reduces the memory requirement from O(N/sup 2/) to O(N) and the operation complexity from O(N/sup 2/) to O(N log N), where N is the number of unknowns. The resultant equations are then solved by the symmetric successive overrelaxation (SSOR) preconditioned conjugate gradient (PCG) method to accelerate iteration, which converges much faster than the conventional CG method. Some typical microstrip circuits and microstrip antenna arrays are analyzed and the good results demonstrate the validity of the proposed algorithm.