Mathematical model of diffraction based on integral equations in the spectral domain

Zykova, M.A.; Lopushenko, V.V.

Авторы: Zykova M.A., Lopushenko V.V.
Журнал: Computational Mathematics and Modeling
Том: 34
Год издания: 2024
Издательство: Consultants Bureau
Местоположение издательства: United States
Первая страница: 125
Последняя страница: 135
DOI: 10.1007/s10598-024-09602-y
Аннотация: A method for solving the volume integral equation of diffraction with a transition to the spatial frequency domain is discussed. For the case of an ellipsoidal scatterer located in free space, by means of the three-dimensional Fourier transform, an integral equation in spectral variables is obtained, and analytical representations for all of its functions are written out. Unlike the classical scheme of singularity extraction, used in solving the equation in spatial variables, the numerical scheme of the proposed method uses an approach based on constructing an “equivalent” Green’s function. In this work, an analytical representation for the Fourier image of such a function is obtained, and it is shown that it does not have a singularity. The discretization of the integral equation is based on Kotelnikov’s theorem with rejection of high-frequency terms. The resulting system of linear algebraic equations was solved by an iterative method using fast algorithms for calculating discrete convolutions. By means of the developed numerical method, a scattering diagram of a homogeneous and layered dielectric spheroid was constructed. It is shown that the diagram can be calculated without additional transformations, directly from the solution of the integral equation.
Добавил в систему: Лопушенко Владимир Васильевич

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Mathematical model of diffraction based on integral equations in the spectral domainстатья

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