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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 7, Pages 1168–1182 (Mi zvmmf10235)  

This article is cited in 5 scientific papers (total in 5 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

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.

DOI: https://doi.org/10.7868/S0044466915070133

Full text: PDF file (268 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:7, 1150–1163

Bibliographic databases:

UDC: 519.6
Received: 03.09.2014

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
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. 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
    4. 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
    5. V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “Adaptivnyi chebyshevskii iteratsionnyi metod”, Matem. modelirovanie, 30:10 (2018), 67–85  mathnet
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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