Numerical method for solving scalar problem of monochromatic wave scattering from a screen with nonlinear transmission conditions
- Authors: Nesterov V.O.1, Tsupak A.A.1
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Affiliations:
- Penza State University
- Issue: No 3 (2025)
- Pages: 13-22
- Section: MATHEMATICS
- URL: https://journals.rcsi.science/2072-3040/article/view/360877
- DOI: https://doi.org/10.21685/2072-3040-2025-3-2
- ID: 360877
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Abstract
Background. The purpose of the study is to develop a numerical approach for solving the scalar diffraction problem on a flat screen with nonlinear transmission conditions. Material and methods. The original problem is reduced to a weakly singular nonlinear integral equation; the collocation method is used to solve the integral equation. Results. The diffraction problem is reduced to a nonlinear integral equation over the screen surface; a numerical method was developed for approximate solving the integral equation. Conclusions. An efficient convergent numerical method was developed and implemented to solve the actual diffraction problem.
About the authors
Vladislav O. Nesterov
Penza State University
Author for correspondence.
Email: nesterovvlad0_o@mail.ru
Postgraduate student
(40 Krasnaya street, Penza, Russia)Aleksey A. Tsupak
Penza State University
Email: altsupak@yandex.ru
Candidate of physical and mathematical sciences, associate professor, associate professor of the sub-department of mathematics and supercomputer modeling
(40 Krasnaya street, Penza, Russia)References
- Smirnov Yu.G., Kondyrev O.V. Integro-differential equations in the problem of scattering of electromagnetic waves on a dielectric body covered with graphene. Differentsialnyye uravneniya = Differential equations. 2024;60(9):1216‒1224. (In Russ.)
- Tsupak A.A. The method of integral equations in the problem of electromagnetic wave propagation in a space filled with a locally inhomogeneous medium, with a graphene layer on the boundary of the inhomogeneity region. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskiye nauki = University proceedings. Volga region. Physical and mathematical sciences. 2024;1. S. 96‒106. (In Russ.)
- Colbrook M.J., Ayton L.J. Do we need non-linear corrections? On the boundary Forchheimer equation in acoustic scattering. Journal of Sound and Vibration. 2021;495:115905. doi: 10.1016/j.jsv.2020.115905
- Smirnov Yu.G., Kondyrev O.V. On the Fredholm property and solvability of a system of integral equations in the conjugacy problem for the Helmholtz equations. Differentsialnyye uravneniya = Differential equations. 2023;59(8):1089‒1097. (In Russ.)
- Kolton D., Kress R. Metody integralnykh uravneniy v teorii rasseyaniya = Methods of integral equations in scattering theory. Transl. from Eng. by Yu.A. Yeremina, E.V. Zakharova; ed. by A.G. Sveshnikov. Moscow: Mir, 1987:311. (In Russ.)
- Vladimirov V.S. Uravneniya matematicheskoy fiziki = Equations of mathematical physics. Moscow: Nauka, 1981:512. (In Russ.)
- Kress R. Linear integral equations. Berlin: Springer-Verlag, 1989:367.
- Tsupak A.A. Convergence of the collocation method for the Lippmann–Schwinger integral equation. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fizikomatematicheskiye nauki = University proceedings. Volga region. Physical and mathematical sciences. 2018;(4):84–93. (In Russ.)
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