Some issues related to the novel spectral acceleration method for the fast computation of radiation/scattering from one-dimensional extremely large scale quasi-planar structures

[1] The novel spectral acceleration (NSA) algorithm has been shown to produce an (Ntot) efficient iterative method of moments for the computation of radiation/scattering from both one-dimensional (1-D) and two-dimensional large-scale quasi-planar structures, where Ntot is the total number of unknowns to be solved. This method accelerates the matrix-vector multiplication in an iterative method of moments solution and divides contributions between points into “strong” (exact matrix elements) and “weak” (NSA algorithm) regions. The NSA method is based on a spectral representation of the electromagnetic Green's function and appropriate contour deformation, resulting in a fast multipole-like formulation in which contributions from large numbers of points to a single point are evaluated simultaneously. In the standard NSA algorithm the NSA parameters are derived on the basis of the assumption that the outermost possible saddle point, ϕs,max, along the real axis in the complex angular domain is small. For given height variations of quasi-planar structures, this assumption can be satisfied by adjusting the size of the strong region Ls. However, for quasi-planar structures with large height variations, the adjusted size of the strong region is typically large, resulting in significant increases in computational time for the computation of the strong-region contribution and degrading overall efficiency of the NSA algorithm. In addition, for the case of extremely large scale structures, studies based on the physical optics approximation and a flat surface assumption show that the given NSA parameters in the standard NSA algorithm may yield inaccurate results. In this paper, analytical formulas associated with the NSA parameters for an arbitrary value of ϕs,max are presented, resulting in more flexibility in selecting Ls to compromise between the computation of the contributions of the strong and weak regions. In addition, a “multilevel” algorithm, decomposing 1-D extremely large scale quasi-planar structures into more than one weak region and appropriately choosing the NSA parameters for each weak region, is incorporated into the original NSA method to improve its accuracy.