Abstract:Background. Mathematical modeling of electromagnetic waves diffraction on screen and bodies of various forms is an important aspect in modern electrodynamics. The objective of this work is to prove the convergence of the Galerkin method for solving the electromagnetic waves diffraction problem on a system of arbitrary located bodies and screens. Material and methods. The statement of the electromagnetic waves diffraction problem on the system of bodies and screens of irregular shapes is considered. The stated problem of diffraction is presented as a system of integral-differential equations; properties of the system are studied using pseudodifferential calculus in Sobolev spaces. Results. The problem of diffraction is formulated; the boundary value problem is reduced to a system of integral-differential equations. To solve the system the authors suggest the numerical method of Galerkin with finite basis functions. The convergence of the Galerkin method is proved. Conclusions. The results of convergence of the Galerkin method for a system consisting of a plane screen and inhomogeneous anisotropic body are obtaned; they are important for further theoretical and numerical studies of the problem.
Keywords:diffraction problem, system of integral-differential equations, the Galerkin method, the basis functions, elliptic operator.
Document Type:
Article
UDC:517.3
Language: Russian
Citation:
Yu. G. Smirnov, M. A. Moskaleva, “Convergence of the Galerkin method in the electromagnetic waves diffraction problem on a system of arbitrary located bodies and screens”, University proceedings. Volga region. Physical and mathematical sciences, 2016, no. 2, 78–86
\Bibitem{SmiMos16}
\by Yu.~G.~Smirnov, M.~A.~Moskaleva
\paper Convergence of the Galerkin method in the electromagnetic waves diffraction problem on a system of arbitrary located bodies and screens
\jour University proceedings. Volga region. Physical and mathematical sciences
\yr 2016
\issue 2
\pages 78--86
\mathnet{http://mi.mathnet.ru/ivpnz246}
\crossref{https://doi.org/10.21685/2072-3040-2016-2-7}
Linking options:
https://www.mathnet.ru/eng/ivpnz246
https://www.mathnet.ru/eng/ivpnz/y2016/i2/p78
This publication is cited in the following 2 articles:
O. S. Skvortsov, A. A. Tsupak, “Chislennoe issledovanie rasseyaniya elektromagnitnoi volny neodnorodnym telom i neploskim idealno provodyaschim ekranom”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2023, no. 3, 46–65
O. S. Skvortsov, A. A. Tsupak, “Numerical Investigation of Electromagnetic Wave Scattering from an Inhomogeneous Solid and a Curvilinear Perfectly Conducting Screen”, Tech. Phys., 68:8 (2023), 187