An Entire-Domain Analysis of Very Large 2-D Scatterers in TM mode Using Gegenbauer Polynomials

We summarize results for using Gegenbauer polynomials as basis functions in the case of the entire-domain 2-D analysis of strips with curvilinear cross section illuminated by a linearly-polarized plane wave. The involved integrals are calculated with 14-digits precision, due to the used singularity-cancellation transformation, for arbitrary cross-section shape. We investigated the error estimate of the surface current approximation due to the defining parameter of the Gegenbauer polynomials and the maximal order of the polynomial for the current approximation. The results for the surface-current approximation with the highest degree of the polynomial basis functions of 7000 are presented. The analyzed curvilinear strip had the total length of the cross section of 2000 wavelengths at the operating frequency in the free space.