# Application of the Method of Moments with RWG Basis Functions in Problems of Diffraction by Plates with Similar Geometries

01 May 2022-Lobachevskii Journal of Mathematics (Lobachevskii Journal of Mathematics)-Vol. 43, Iss: 5, pp 1232-1244

About: This article is published in Lobachevskii Journal of Mathematics.The article was published on 2022-05-01. It has received 1 citations till now. The article focuses on the topics: Mathematics & Diffraction.

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TL;DR: In this paper, the electric field integral equation (EFIE) is used with the moment method to develop a simple and efficient numerical procedure for treating problems of scattering by arbitrarily shaped objects.

Abstract: The electric field integral equation (EFIE) is used with the moment method to develop a simple and efficient numerical procedure for treating problems of scattering by arbitrarily shaped objects. For numerical purposes, the objects are modeled using planar triangular surfaces patches. Because the EFIE formulation is used, the procedure is applicable to both open and closed surfaces. Crucial to the numerical formulation is the development of a set of special subdomain-type basis functions which are defined on pairs of adjacent triangular patches and yield a current representation free of line or point charges at subdomain boundaries. The method is applied to the scattering problems of a plane wave illuminated flat square plate, bent square plate, circular disk, and sphere. Excellent correspondence between the surface current computed via the present method and that obtained via earlier approaches or exact formulations is demonstrated in each case.

4,835 citations

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TL;DR: In this paper, a matrix splitting algorithm is developed to break up the texture limit, which splits the huge matrix into multiple, tiny matrixes, each of which can be fit into one texture.

Abstract: The graphics processing unit (GPU) has been used to speed up the conventional method of moments (MoM) calculations for electromagnetic scattering from arbitrary three-dimensional conducting objects. The acceleration ratio of filling impedance matrix has reached 30, while the total acceleration ratio (including iteration) is about 20. Moreover, a matrix splitting algorithm is developed to break up the texture limit. It splits the huge matrix into multiple, tiny matrixes, each of which can be fit into one texture. Then, the system memory can be used to store all the elements of the impedance matrix, making it possible to deal with electrically large problems, since the capacity of video card's memory is no longer a limit.

97 citations

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TL;DR: Three less well-known and somewhat novel methods are offered, namely the embedding method, a random walk approach, and the technique of functionally-invariant solutions, which would be of interest even to specialists in the field.

39 citations

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TL;DR: In this paper, the problem of diffraction of a plane TE-polarized electromagnetic wave by gaps between metal plates located in the same plane is investigated, and the diffraction problem is formulated as a boundary value problem for the Helmholtz equation with the boundary conditions on metal and a given asymptotic behavior at the edges of the screens.

Abstract: The problem of diffraction of a plane TE-polarized electromagnetic wave by gaps between metal plates located in the same plane is investigated. The diffraction problem is formulated as a boundary-value problem for the Helmholtz equation with the boundary conditions on metal and a given asymptotic behavior at the edges of the screens. The solutions are sought in the class of waves propagating to infinity. The problem under consideration is reduced to an integral equation with a strongly singular kernel with respect to the trace of the electric field vector in the gap. In turn, the integral equation is reduced to an infinite system of linear algebraic equations with respect to the expansion coefficients of the derivative of the sought function. Some singular integrals involving generalized Chebyshev polynomials are analytically calculated.

15 citations