Volume Singular Integral Equations for Problems of Low-Frequency Scattering of Electromagnetic Waves in Anisotropic Structures

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Abstract
This paper deals with volume singular integral equations describing the problems of low-frequency scattering of electromagnetic waves in bounded three-dimensional anisotropic structures. The spectrum of integral operators is studied. The domain of the operator spectrum in the complex plane for the low-frequency case is presented explicitly. The generalized simple iteration method is described for the application of which it is necessary to know the area of the operator spectrum in the complex plane. The collocation method on a uniform grid is used to discretize the integral equations. Using a fast discrete Fourier transform, this allows constructing an algorithm for fast multiplication of the matrix of a system of linear equations by a vector. The results of numerical solution of the considered problems are given.

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