Theory of integral equations of diffraction on an open cylindrical surface
https://doi.org/10.34680/2076-8052.2023.5(134).858-862
Abstract
A new, mathematically efficient method for solving the vector equation of diffraction on an open cylindrical surface is proposed. The method is based on the allocation of the main operator, the definition of functional spaces and the reduction of the operator equation to the Fredholm equation of the second kind. Sobolev spaces are used as ones that take into account the Meixner condition on the edge. In the selected spaces, the main operator is bounded and invertible; the inverse operator is also bounded. A projection method for solving operator equations has been developed.
About the Authors
S. I. Eminov
Yaroslav-the-Wise Novgorod State University
Russian Federation
Russian Federation
Veliky Novgorod
A. V. Sochilin
Yaroslav-the-Wise Novgorod State University
Russian Federation
Russian Federation
Veliky Novgorod
M. A. Zakharov
Yaroslav-the-Wise Novgorod State University
Russian Federation
Russian Federation
Veliky Novgorod
R. V. Petrov
Yaroslav-the-Wise Novgorod State University
Russian Federation
Russian Federation
Veliky Novgorod
References
1. Vasil'ev E. N. Vozbuzhdenie tel vrashcheniia [Excitation of bodies of revolution]. Moscow, Radio i sviaz', 1987. 272 p.
2. Davydov A. G., Zakharov E. V., Pimenov Iu. V. Metod chislennogo resheniia zadach difraktsii elektromagnitnykh voln na nezamknutykh poverkhnostiakh proizvol'noi formy [A numerical method for solving the problems of electromagnetic wave diffraction on freeform open surfaces] // Doklady Akademii nauk. 1984. 276(1). 96-100.
3. Eminov S. I. Analytical inversion of the operator matrix for the problem of diffraction by a cylindrical segment in Sobolev spaces // Computational Mathematics and Mathematical Physics. 2021. 61(3). 424-430. DOI: 10.1134/S0965542521030052
Review
For citations:
Eminov S.I., Sochilin A.V., Zakharov M.A., Petrov R.V. Theory of integral equations of diffraction on an open cylindrical surface. Title in english. 2023;(5(134)):858-862. (In Russ.) https://doi.org/10.34680/2076-8052.2023.5(134).858-862
Views:
34
Email this article 