In this research, a sub-array preconditioner is applied to improve the convergence of conjugate gradient (CG) iterative solver in the fast multipole method and fast Fourier transform (FMM-FFT) implementation on a large-scale finite periodic array antenna with arbitrary geometry elements. The performance of the sub-array preconditioner is compared with the near-group preconditioner in the array antenna analysis. It is found that the near-group preconditioner achieves a little better convergence, while the sub-array preconditioner can be easily constructed and programmed with less CPU-time. The efficiency of the CG-FMM-FFT with high efficient preconditioner has been demonstrated in numerical analysis of a finite periodic array antenna.

This paper presents method that offers the fast and accurate analysis of large-scale periodic array antennas by conjugate-gradient fast Fourier transform (CG-FFT) combined with an equivalent sub-array preconditioner. Method of moments (MoM) is used to discretize the electric field integral equation (EFIE) and form the impedance matrix equation. By properly dividing a large array into equivalent sub-blocks level by level, the impedance matrix becomes a structure of Three-level Block Toeplitz Matrices. The Three-level Block Toeplitz Matrices are further transformed to Circulant Matrix, whose multiplication with a vector can be rapidly implemented by one-dimension (1-D) fast Fourier transform (FFT). Thus, the conjugate-gradient fast Fourier transform (CG-FFT) is successfully applied to the analysis of a large-scale periodic dipole array by speeding up the matrix-vector multiplication in the iterative solver. Furthermore, an equivalent sub-array preconditioner is proposed to combine with the CG-FFT analysis to reduce iterative steps and the whole CPU-time of the iteration. Some numerical results are given to illustrate the high efficiency and accuracy of the present method.