Scattering and propagation of the TE/TM waves on pre-fractal impedance grating in numerical results

Nesvit, Kateryna

doi:10.1109/eucap.2014.6902400

Cited by 7 publications

(3 citation statements)

References 3 publications

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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].…”

Section: Origins Of Researchmentioning

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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Section: Origins Of Researchmentioning

confidence: 99%

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

2019

MAMM

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“…We believe that a better understanding of Schrödinger operators with such singular potentials (supported by fractal sets) might shed some additional light on the above problem. This was the main motivation for the present work, although the results obtained here might be of some relevance to the study of fractal antennae, apertures, screens, and transducers (see, e.g, [8,9,10,15,32,47] and the references therein), especially in the case of impedance (Robin) boundary conditions (see [19,33,34,35]).…”

Section: Introductionmentioning

confidence: 99%

On estimates for the number of negative eigenvalues of two-dimensional Schrödinger operators with potentials supported by Lipschitz curves

Karuhanga

2017

Journal of Mathematical Analysis and Applications

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“…In cases where the integrand exhibits a singularity of one of the above types, this further complicates the evaluation of the integral. Such integrals arise in applications in electromagnetics [17,18] and electromagnetic shielding problems [10]. In the present work we focus on the frequency-domain, wave-enriched boundary integral formulations as a particular example to motivate this work.…”

Section: Introductionmentioning

confidence: 99%

Quadrature Methods for Highly Oscillatory Singular Integrals

Jing¹

2021

JCM

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Scattering and propagation of the TE/TM waves on pre-fractal impedance grating in numerical results

Cited by 7 publications

References 3 publications

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

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

On estimates for the number of negative eigenvalues of two-dimensional Schrödinger operators with potentials supported by Lipschitz curves

Quadrature Methods for Highly Oscillatory Singular Integrals

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