Analytical regularization method for electromagnetic wave diffraction by periodic wavy obstacles: Perfectly conductive screen and two media boundary surface

Abstract

New strong in mathematical sense and numerically efficient methods for numerical simulation of two-dimensional boundary value problems (BVP) of electromagnetic wave diffraction by perfectly conductive periodic wavy screen or by periodic wavy boundary surface between two media are suggested. The initial BVPs are equivalently reduced to infinite algebraic systems of the second kind: (I+H)x=b in Hilbert space of square summable sequences, where H is compact and I is identic operators respectively. Such equation can be solved numerically with any necessary accuracy by means of truncation method, which is known as numerically stable one for equations of the second kind. The approach used is based on our ideas [1-6]. The initial BVPs are, at first, reduced to corresponding integral or integral-differential equations - see [4-6]. At second, investigation of singular properties of kernels of their integral operators gave the possibility to construct the relevant two-sided regularizators [3, 4] and to obtain the algebraic system of the second kind. The essential part of the methods efficient numerical implementation is application of Fast Fourier Transform, and its analytical acceleration [1, 3] for the kernels produced by quasi-periodic Green's function on the contours of integration, as well as fast calculation of Green's function itself by means of systematic analytical extraction and summation of slow convergent parts of Poisson's series for Green's function [1-3, 6]. © 2013 Elsevier B.V., All rights reserved.