In this paper, an improved CBFM/p-FFT algorithm is presented, which can be applied to solve electromagnetic scattering problems of large-scale periodic composite metallic/dielectric arrays, even when the array has electrically small periodicity or separating distance. Using characteristic basis function method (CBFM), scattering characteristics of any inhomogeneous targets can be represented by special responses derived from a set of incident plane waves (PWs). In order to reserve the dominant scattering characteristics of the targets and remove the redundancy of the overfull responses, a singular value decomposition (SVD) procedure is applied, then, new series of basis functions are built based on the left singular vectors after SVD whose corresponding singular values beyond a predefined threshold. However, the algorithm of CBFM combined with method of moments (MoM) still requires a lot of memory and CPU resources to some large scale problems, so the precorrected-fast Fourier transform (p-FFT) method is applied based on the novel built basis functions, with which, the required memory and solve time for solution can be reduced in an extraordinary extent. For a near correction technique is applied to process the interactions between cells placed within a distance less than a predefined near-far field threshold, arrays with electrically small periodicity can be analyzed accurately. Moreover, the incomplete LU factorization with thresholding (ILUT) preconditioner is applied to improve the condition number of the combined algorithm, which improves the convergence speed greatly.
Joshua Le-Wei Li,
"Scattering Analysis of Periodic Arrays Using Combined Cbf/P-FFT Method," Progress In Electromagnetics Research,
Vol. 115, 131-146, 2011. doi:10.2528/PIER11020601
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