Loading [MathJax]/jax/output/SVG/config.js
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

Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 7, Pages 1168–1182
DOI: https://doi.org/10.7868/S0044466915070133 (Mi zvmmf10235) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Multigrid method for elliptic equations with anisotropic discontinuous coefficients

V. T. Zhukov, N. D. Novikova, O. B. Feodoritova

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia
Full-text PDF (268 kB) Citations (13)
References:
PDF
HTML
DOI: https://doi.org/10.7868/S0044466915070133
Abstract: For difference elliptic equations, an algorithm based on Fedorenko’s multigrid method is constructed. The algorithm is intended for solving three-dimensional boundary value problems for equations with anisotropic discontinuous coefficients on parallel computers. Numerical results confirming the performance and parallel efficiency of the multigrid algorithm are presented. These qualities are ensured by using, as a multigrid triad, the standard Chebyshev iteration for coarsest grid equations, Chebyshev-type smoothing explicit iterative procedures, and intergrid transfer operators in problem-dependent form.
Key words: three-dimensional elliptic equations, anisotropic discontinuous coefficients, multigrid method, Chebyshev iteration method, parallel implementation.
Received: 03.09.2014
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 7, Pages 1150–1163
DOI: https://doi.org/10.1134/S0965542515070131
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “Multigrid method for elliptic equations with anisotropic discontinuous coefficients”, Zh. Vychisl. Mat. Mat. Fiz., 55:7 (2015), 1168–1182; Comput. Math. Math. Phys., 55:7 (2015), 1150–1163
Citation in format AMSBIB
\Bibitem{ZhuNovFeo15}
\by V.~T.~Zhukov, N.~D.~Novikova, O.~B.~Feodoritova
\paper Multigrid method for elliptic equations with anisotropic discontinuous coefficients
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2015
\vol 55
\issue 7
\pages 1168--1182
\mathnet{http://mi.mathnet.ru/zvmmf10235}
\crossref{https://doi.org/10.7868/S0044466915070133}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3372637}
\elib{https://elibrary.ru/item.asp?id=23661500}
\transl
\jour Comput. Math. Math. Phys.
\yr 2015
\vol 55
\issue 7
\pages 1150--1163
\crossref{https://doi.org/10.1134/S0965542515070131}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000358644300007}
\elib{https://elibrary.ru/item.asp?id=23994002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84938152135}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf10235
  • https://www.mathnet.ru/eng/zvmmf/v55/i7/p1168
    • This publication is cited in the following 13 articles:
    1. V. A. Gordin, D. A. Shadrin, “Compact approximation of a two-dimensional boundary value problem for elliptic equations of the 2nd order with a discontinuous coefficient”, Math. Models Comput. Simul., 15:5 (2023), 920–943  mathnet  crossref  crossref  mathscinet
    2. Pan K., Wu X., Hu H., Yu Yu., Li Zh., “A New Fv Scheme and Fast Cell-Centered Multigrid Solver For 3D Anisotropic Diffusion Equations With Discontinuous Coefficients”, J. Comput. Phys., 449 (2022), 110794  crossref  mathscinet  isi  scopus
    3. Olga Borisovna Feodoritova, Natalia Dmitrievna Novikova, Mikhail Mikhailovich Krasnov, Victor Timofeevich Zhukov, “Multigrid method for numerical modelling of high temperature superconductors”, MathMon, 53 (2022), 72  crossref
    4. V. T. Zhukov, O. B. Feodoritova, “Algoritm rascheta fizicheskikh protsessov v vysokotemperaturnykh sverkhprovodnikakh”, Preprinty IPM im. M. V. Keldysha, 2020, 124, 27 pp.  mathnet  crossref
    5. O B Feodoritova, V T Zhukov, “An adaptive multigrid on block-structured grids”, J. Phys.: Conf. Ser., 1640:1 (2020), 012020  crossref
    6. V. T. Zhukov, V. M. Krasnov, M. M. Krasnov, N. D. Novikova, O. B. Feodoritova, “On numerical simulation of physical processes in high-temperature superconductors”, Keldysh Institute preprints, 2019, 129–21  mathnet  mathnet  crossref
    7. V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “Chebyshevskie iteratsii s adaptivnym utochneniem nizhnei granitsy spektra matritsy”, Preprinty IPM im. M. V. Keldysha, 2018, 172, 32 pp.  mathnet  crossref  elib
    8. V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “An adaptive Chebyshev iterative method”, Math. Models Comput. Simul., 11:3 (2019), 426–437  mathnet  crossref
    9. V. T. Zhukov, O. B. Feodoritova, “On development of parallel algorithms for the solution of parabolic and elliptic equations”, J. Math. Sci. (N. Y.), 254:5 (2021), 606–624  mathnet  crossref  mathscinet
    10. O B Feodoritova, M M Krasnov, V T Zhukov, “Adaptive technique for Chebyshev-Based solvers for three-dimensional elliptic equations”, J. Phys.: Conf. Ser., 1103 (2018), 012012  crossref
    11. V. T. Zhukov, M. M. Krasnov, N. D. Novikova, O. B. Feodoritova, “Algebraicheskii mnogosetochnyi metod c adaptivnymi sglazhivatelyami na osnove mnogochlenov Chebysheva”, Preprinty IPM im. M. V. Keldysha, 2016, 113, 32 pp.  mathnet  crossref
    12. Feodoritova O.B. Novikova N.D. Zhukov V.T., “Multigrid Method For Diffusion Equations Based on Adaptive Smoothing”, Math. Montisnigri, 36 (2016), 14–26  mathscinet  zmath  isi
    13. V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “On the solution of evolution equations based on multigrid and explicit iterative methods”, Comput. Math. Math. Phys., 55:8 (2015), 1276–1289  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Statistics & downloads:
    Abstract page:478
    Full-text PDF :110
    References:92
    First page:20
     
      Contact us:
    math-net2025_04@mi-ras.ru     		 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025