Mathematical Model of Wave Scattering by an Impedance Grating1

Kostenko, A. V.

doi:10.1007/s10559-015-9727-8

Cited by 6 publications

(2 citation statements)

References 7 publications

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“…Найбільша кількість числових результантів була отримана для задач дифракції періодичних та неперіодичних систем стрічок, з однаковою величиною поверхневого імпедансу на обох сторонах стрічок. Завдяки універсальності методу параметричного подання інтегральних перетворень у періодичному випадку були отримані три різні моделі для опису цього випадку: дві на базі сингулярних інтегральних рівнянь різного типу та одна гіперсинулярна модель [15][16][17]. Математичне обґрунтовування чисельного розв'язання таких рівнянь було дано у роботах [18][19][20].…”

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Mathematical Model of Wave Diffraction by the System of Stripes With Different Values of Surface Impedance

Dushkin

Мельник

2021

JNAM

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A mathematical model of diffraction of E-polarized and H-polarized waves on a finite system of not perfectly conducting tapes is obtained. The value of the surface impedance on the two sides of the stripes is different. The initial boundary value problem for the Helmholtz equation with boundary conditions of the third kind was reduced to a system of boundary integral equations. This system of boundary integral equations consists of singular integral equations of the first kind and integral equations of the second kind with a logarithmic singularity. The method of parametric representation of integral operator was used to perform transformations. The values of the physical characteristics of the process are expressed through the solutions of the obtained systems of integral equations. Numerical solution of these equations is performed using a computational scheme based on the discrete singularities method.

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Section: вступunclassified

Mathematical Model of Wave Diffraction by the System of Stripes With Different Values of Surface Impedance

Dushkin

Мельник

2021

JNAM

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“…By solving this system, the approximate values of the maineld characteristics are determined. The method of parametric representations of integral operators makes it possible to obtain systems of integral equations of other types [29], [30]. In particular, the original boundary-value problem was reduced to a system consisting of hypersingular integral equations of the second kind and the Fredholm integral equation of the second kind [32], [37].…”

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confidence: 99%

Discrete mathematical model of the scattering process of E-polarized wave on a periodic impedance grating

2019

MAMM

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The method of numerical modeling of wave scattering by periodic impedance grating is considered. In the case of a harmonic dependence of the field on time and the uniformity of the structure along a certain axis, the three-dimensional problem reduces to considering of two 2D problems for the components of the E-polarized and H-polarized waves. The signle nonzero component of the electric field created by the incident E-polarized wave is the solution of the boundary value problem for the Helmholtz equation with Robin boundary conditions. It follows from the physical formulation of the problem that its solutions satisfy the Floquet quasiperiodicity condition, the condition of finiteness of energy in any bounded region of the plane. Also, the difference between the total and incident fields satisfies the Sommerfeld radiation condition. Following the ideas of the works of Yu.V. Gandel, using the method of parametric representations of integral operators, the boundary-value problem reduces to two systems of integral equations. The first one is the system of singular equations of the first kind with additional integral conditions. The second system consists of the Fredholm boundary integral equations of the second kind with a logarithmic singularity in the integrand. A discrete model for various values of the discretization parameter is equivalent to systems of singular integral equations. By solving these equations, approximate values of the main field characteristics are determined. The method of parametric representations of integral operators makes it possible to obtain systems of integral equations of other types. In particular, the initial boundary-value problem reduces to a system consisting of hypersingular integral equations of the second kind and the Fredholm integral equation of the second kind. A numerical experiment was conducted for cases of different location of tapes. Calculations were performed for the proposed model and the model based on hypersingular equations. They showed the closeness of the obtained results in a wide range of parameters studied.

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A Numerical Method for Solving a System of Hypersingular Integral Equations of the Second Kind

Kostenko

2016

Cybern Syst Anal

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Mathematical Model of Wave Scattering by an Impedance Grating1

Cited by 6 publications

References 7 publications

Mathematical Model of Wave Diffraction by the System of Stripes With Different Values of Surface Impedance

Mathematical Model of Wave Diffraction by the System of Stripes With Different Values of Surface Impedance

Discrete mathematical model of the scattering process of E-polarized wave on a periodic impedance grating

A Numerical Method for Solving a System of Hypersingular Integral Equations of the Second Kind

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