The Approximate Method for Solving the Boundary Integral Equations of the Problem of Wave Scattering by Superconducting Lattice

V., Gandel Yu.; Dushkin, V.D.

doi:10.12691/ajams-2-6-3

AJAMS

2014

DOI: 10.12691/ajams-2-6-3

|View full text |Cite

The Approximate Method for Solving the Boundary Integral Equations of the Problem of Wave Scattering by Superconducting Lattice

Gandel Yu. V.¹,

V.D. Dushkin²

Abstract: In this article the method for numerical solution of boundary integral equations of the original problem is proposed. This method is one of the modifications of Nystrom-type methods; particularly the method of discrete vortices. The convergence of the numerical solutions to the exact solution of the problem is guaranteed by propositions proved in this article. Also, the rate of convergence of the approximate solutions to the exact solution had been found.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2019

2021

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

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

Dushkin

Мельник

2021

JNAM

View full text Add to dashboard Cite

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.

show abstract

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

Dushkin

Мельник

2021

JNAM

View full text Add to dashboard Cite

show abstract

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

2019

MAMM

View full text Add to dashboard Cite

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.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

The Approximate Method for Solving the Boundary Integral Equations of the Problem of Wave Scattering by Superconducting Lattice

Cited by 2 publications

References 9 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

Contact Info

Product

Resources

About