Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






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


Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 7, Pages 1197–1206 (Mi zvmmf4718)  

This article is cited in 7 scientific papers (total in 7 papers)

Method of boundary integral equations as applied to the numerical solution of the three-dimensional Dirichlet problem for the laplace equation in a piecewise homogeneous medium

E. V. Zakharov, A. V. Kalinin

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia

Abstract: A Dirichlet problem is considered in a three-dimensional domain filled with a piecewise homogeneous medium. The uniqueness of its solution is proved. A system of Fredholm boundary integral equations of the second kind is constructed using the method of surface potentials, and a system of boundary integral equations of the first kind is derived directly from Green's identity. A technique for the numerical solution of integral equations is proposed, and results of numerical experiments are presented.

Key words: Dirichlet problem for the Laplace equation, piecewise homogeneous medium, method of boundary integral equations.

Full text: PDF file (1148 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2009, 49:7, 1141–1150

Bibliographic databases:

UDC: 519.632.4
Received: 17.10.2008
Revised: 15.12.2008

Citation: E. V. Zakharov, A. V. Kalinin, “Method of boundary integral equations as applied to the numerical solution of the three-dimensional Dirichlet problem for the laplace equation in a piecewise homogeneous medium”, Zh. Vychisl. Mat. Mat. Fiz., 49:7 (2009), 1197–1206; Comput. Math. Math. Phys., 49:7 (2009), 1141–1150

Citation in format AMSBIB
\Bibitem{ZakKal09}
\by E.~V.~Zakharov, A.~V.~Kalinin
\paper Method of boundary integral equations as applied to the numerical solution of the three-dimensional Dirichlet problem for the laplace equation in a~piecewise homogeneous medium
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
\vol 49
\issue 7
\pages 1197--1206
\mathnet{http://mi.mathnet.ru/zvmmf4718}
\transl
\jour Comput. Math. Math. Phys.
\yr 2009
\vol 49
\issue 7
\pages 1141--1150
\crossref{https://doi.org/10.1134/S0965542509070070}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000268295700007}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70349971420}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf4718
  • http://mi.mathnet.ru/eng/zvmmf/v49/i7/p1197

    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. Denisov A.M., Zakharov E.V., Kalinin A.V., Kalinin V.V., “Numerical methods for solving some inverse problems of heart electrophysiology”, Differ. Equ., 45:7 (2009), 1034–1043  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. A. M. Denisov, E. V. Zakharov, A. V. Kalinin, V. V. Kalinin, “Numerical solution of an inverse electrocardiography problem for a medium with a piecewise-constant electrical conductivity coefficient”, Comput. Math. Math. Phys., 50:7 (2010), 1172–1177  mathnet  crossref  mathscinet  adsnasa  isi
    3. S. V. Gavrilov, A. M. Denisov, “A numerical method for determining the inhomogeneity boundary in the Dirichlet problem for the Laplace equation in a piecewise-homogeneous medium”, Comput. Math. Math. Phys., 50:8 (2010), 1391–1398  mathnet  crossref  mathscinet  adsnasa  isi
    4. A. M. Denisov, E. V. Zakharov, A. V. Kalinin, “Method for determining projection of the arrhythmogenic focus on a heart surface based on solution of the inverse electrocardiography problem”, Math. Models Comput. Simul., 4:6 (2012), 535–540  mathnet  crossref  mathscinet  elib
    5. Klepka S.P., Lastovetskii A.E., Pavlov G.L., “Matematicheskoe modelirovanie elektrostaticheskikh polei v sistemakh blizhnei lokatsii”, Elektromagnitnye volny i elektronnye sistemy, 17:3 (2012), 4–10  elib
    6. Zakharov E.V. Kalinin A.V., “Numerical Solution of the Three-Dimensional Dirichlet Problem for Inhomogeneous Media by the Method of Integral Equations”, Differ. Equ., 49:9 (2013), 1160–1167  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. N. Tynda, K. A. Timoshenkov, “Primenenie metoda granichnykh integralnykh uravnenii k chislennomu resheniyu ellipticheskikh kraevykh zadach v $\mathbb{R}^3$”, Zhurnal SVMO, 22:3 (2020), 319–332  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:1098
    Full text:334
    References:46
    First page:41

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