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

Abstract

In this paper we compare different iterative techniques enhanced by the CBFM, that are used to analyze finite arrays of disjoint antenna elements. These are based on the stationary-type methods (Jacobi, Gauss-Seidel, macro-block Jacobi), the nonstationary GMRES and the hybrid alternating GMRES-Jacobi (AGJ) method which 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 increased presence of the inter-element 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.

Use of the Adaptive Cross Approximation for the Efficient Computation of the Reduced Matrix with the Characteristic Basis Function Method

“…The interest in the use of techniques dealing with Macro Basis Functions (MBFs) [7][8][9][10][11][12][13][14][15][16][17] has increased sharply during the last decade, based on the computational advantages of reducing the effective numerical size of the problems under analysis. This family of methods requires the computation of a new set of basis functions defined on a number of blocks in which the scenario has been previously partitioned.…”

“…In [15], the CBFs are used as a sparse base over which a Compressive Sensing approach is used to analyze the bistatic RCS of 3D targets. The work described in [16] makes use of CBFs in order to improve the alternating GMRES-Jacobi (AGJ) iterative solver, where the reduced system is built based on the previous iterations. The authors of [17] have presented a fast technique for the computation of the CBFs, making use of a Sparse Approximate Inverse (SAI) matrix used as a direct operator to obtain an estimation of the currents induced by a large number of plane wave sources on each block.…”