Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
General information
Latest issue
Impact factor

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Zh. Vychisl. Mat. Mat. Fiz.:

Personal entry:
Save password
Forgotten password?

Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 8, Pages 1319–1331 (Mi zvmmf10078)  

This article is cited in 9 scientific papers (total in 9 papers)

Scalar problem of plane wave diffraction by a system of nonintersecting screens and inhomogeneous bodies

M. Yu. Medvedik, Yu. G. Smirnov, A. A. Tsupak

Penza State University, ul. Krasnaya 40, Penza, 440026, Russia

Abstract: The scalar problem of plane wave diffraction by a system of bodies and infinitely thin screens is considered in a quasi-classical formulation. The solution is sought in the classical sense but is defined not in the entire space $\mathbb{R}^3$ but rather everywhere except for the screen edges. The original boundary value problem for the Helmholtz equation is reduced to a system of weakly singular integral equations in the regions occupied by the bodies and on the screen surfaces. The equivalence of the integral and differential formulations is proven, and the solvability of the system in the Sobolev spaces is established. The integral equations are approximately solved by the Bubnov–Galerkin method. The convergence of the method is proved, its software implementation is described, and numerical results are presented.

Key words: scalar problem of plane wave diffraction, Helmholtz equation, method of singular integral equations in Sobolev space, Galerkin method, convergence of numerical scheme, software implementation.

DOI: https://doi.org/10.7868/S0044466914080109

Full text: PDF file (306 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2014, 54:8, 1280–1292

Bibliographic databases:

UDC: 519.634
MSC: 78A45
Received: 24.01.2014

Citation: M. Yu. Medvedik, Yu. G. Smirnov, A. A. Tsupak, “Scalar problem of plane wave diffraction by a system of nonintersecting screens and inhomogeneous bodies”, Zh. Vychisl. Mat. Mat. Fiz., 54:8 (2014), 1319–1331; Comput. Math. Math. Phys., 54:8 (2014), 1280–1292

Citation in format AMSBIB
\by M.~Yu.~Medvedik, Yu.~G.~Smirnov, A.~A.~Tsupak
\paper Scalar problem of plane wave diffraction by a system of nonintersecting screens and inhomogeneous bodies
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2014
\vol 54
\issue 8
\pages 1319--1331
\jour Comput. Math. Math. Phys.
\yr 2014
\vol 54
\issue 8
\pages 1280--1292

Linking options:
  • http://mi.mathnet.ru/eng/zvmmf10078
  • http://mi.mathnet.ru/eng/zvmmf/v54/i8/p1319

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. G. Smirnov, A. A. Tsupak, “Method of Integral Equations in the Scalar Problem of Diffraction on a System Consisting of a “soft” and a “hard” Screen and An Inhomogeneous Body”, Differ. Equ., 50:9 (2014), 1150–1160  crossref  mathscinet  zmath  isi  elib  scopus
    2. Y. G. Smirnov, A. A. Tsupak, “Integrodifferential equations of the vector problem of electromagnetic wave diffraction by a system of nonintersecting screens and inhomogeneous bodies”, Adv. Math. Phys., 2015, 945965  crossref  mathscinet  zmath  isi  elib  scopus
    3. S. A. Manenkov, “Two approaches to solving the problem of diffraction by a cylindrical body with a coordinate-dependent refractive index”, J. Commun. Technol. Electron., 61:11 (2016), 1237–1244  crossref  isi  elib  scopus
    4. M. Yu. Medvedik, Yu. G. Smirnov, A. A. Tsupak, D. V. Valovik, “Vector problem of electromagnetic wave diffraction by a system of inhomogeneous volume bodies, thin screens, and wire antennas”, J. Electromagn. Waves Appl., 30:8 (2016), 1086–1100  crossref  isi  elib  scopus
    5. Yu. G. Smirnov, A. A. Tsupak, “On the Fredholm property of the electric field equation in the vector diffraction problem for a partially screened solid”, Differ. Equ., 52:9 (2016), 1199–1208  crossref  mathscinet  zmath  isi  elib  scopus
    6. Yu. G. Smirnov, M. Yu. Medvedik, A. A. Tsupak, M. A. Moskaleva, “Zadacha difraktsii akusticheskikh voln na sisteme tel, ekranov i antenn”, Matem. modelirovanie, 29:1 (2017), 109–118  mathnet  elib
    7. E. H. Khalilov, “Substantiation of the collocation method for one class of systems of integral equations”, Ukr. Math. J., 69:6 (2017), 955–969  crossref  mathscinet  isi  scopus
    8. Yu. G. Smirnov, A. A. Tsupak, “Existence and uniqueness theorems in electromagnetic diffraction on systems of lossless dielectrics and perfectly conducting screens”, Appl. Anal., 96:8 (2017), 1326–1341  crossref  mathscinet  zmath  isi  scopus
    9. E. H. Khalilov, “Constructive method for solving a boundary value problem with impedance boundary condition for the Helmholtz equation”, Differ. Equ., 54:4 (2018), 539–550  crossref  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:219
    Full text:71
    First page:6

    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021