A fast and efficient multi-dimensional adaptive sampling method (ASM) based on Stoer-Bulirsch (S-B) algorithm for frequency selective surface (FSS) analysis and design is presented in this paper. The multivariate rational function is established according to the functional relation of the scattering parameters with frequency and direction of incident wave, medium parameters and geometry dimensions of FSS structure, et al. In order to evaluate the values of the multivariate rational function fully automatically without determining the coefficients of the targeted rational interpolant, the one-dimensional S-B algorithm is expanded into multidimensional method. The sampling points in each dimension are chosen at the areas of maximum error in an adaptive way. The recursive interpolation results of one dimension are used as the initial values of next dimension in the recursive tabular until n-dimension recursive interpolation is accomplished. The initial values of recursive algorithm are calculated by spectral domain method of moments (MoM) at every sample point. The current distribution of FSS cell is predicted by Rao-Wilton-Glisson (RWG) subdomain basis functions which are applicable for arbitrarily shape elements. Four examples, including FSS with the eight-legged, cross and ring elements and FSS radome enclosed antennas, are considered to demonstrate the feasibility of applying the multi-dimensional ASM to analysis and optimal design of FSS. Numerical results show that the proposed method is superior in computation efficiency compared to the direct MoM. Good agreement between the proposed technique and the direct MoM is observed.
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