Loading [MathJax]/jax/output/SVG/config.js
University proceedings. Volga region. Physical and mathematical sciences
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



University proceedings. Volga region. Physical and mathematical sciences:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


University proceedings. Volga region. Physical and mathematical sciences, 2016, Issue 2, Pages 78–86
DOI: https://doi.org/10.21685/2072-3040-2016-2-7
(Mi ivpnz246)
 

This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

Convergence of the Galerkin method in the electromagnetic waves diffraction problem on a system of arbitrary located bodies and screens

Yu. G. Smirnov, M. A. Moskaleva

Penza State University, Penza
Full-text PDF (415 kB) Citations (2)
References:
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
Citation in format AMSBIB
\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:
    1. 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  mathnet  crossref
    2. 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  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    University proceedings. Volga region. Physical and mathematical sciences
    Statistics & downloads:
    Abstract page:54
    Full-text PDF :18
    References:19
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025