Comparison of CBFM-Enhanced Iterative Methods for MoM-Based Finite Antenna Array Analysis

Abstract

In this article, we compare different iterative techniques enhanced by the CBFM, which are used to analyze finite arrays of disjoint antenna elements. These are based on the stationary-type methods (Jacobi, Gauss–Seidel, and macroblock Jacobi), the nonstationary GMRES, and the hybrid alternating GMRES-Jacobi (AGJ) method that combines these two types. In each iteration, the reduced CBFM system is constructed based on the previous iterates, the solution of which is used to update the solution vector in the next iteration with improved accuracy. In this way, the convergence of the classical iterative techniques can be greatly improved. The convergence rates and computational costs of the CBFM-enhanced iterative methods are analyzed by considering several MoM-based problems. The GMRES-based method, which employs the block-Jacobi preconditioner, outperforms the other methods when the MoM matrix is ill-conditioned. For well-conditioned MoM matrices with reduced diagonal dominance due to the increased presence of the interelement coupling effects, the AGJ method or the methods based on the stationary-type iterations may require smaller computational effort to converge to the desired solution accuracy in comparison to the GMRES-based approach.