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Matem. Mod., 2014, Volume 26, Number 9, Pages 126–140 (Mi mm3520)  

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

Multigrid for anisotropic diffusion problems based on adaptive Chebyshev's smoothers

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

Keldysh Institute of Applied Mathematics of RAS, Moscow

Abstract: We propose an efficient multigrid algorithm for solving anisotropic elliptic difference equations. The algorithm is based on the explicit Chebyshev iterations for solution of the coarsest grid equations and for construction of smoothing procedures. We develop the adaptive smoothers for anisotropic problems, and show that it provides efficiency of the multigrid algorithm and scalability in parallel implementation.

Keywords: three-dimensional anisotropic diffusion, multigrid algorithm, Chebyshev's iterations, adaptive smoother, parallel implementation.

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English version:
Mathematical Models and Computer Simulations, 2015, 7:2, 117–127

UDC: 519.6
Received: 24.06.2013

Citation: V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “Multigrid for anisotropic diffusion problems based on adaptive Chebyshev's smoothers”, Matem. Mod., 26:9 (2014), 126–140; Math. Models Comput. Simul., 7:2 (2015), 117–127

Citation in format AMSBIB
\Bibitem{ZhuNovFeo14}
\by V.~T.~Zhukov, N.~D.~Novikova, O.~B.~Feodoritova
\paper Multigrid for anisotropic diffusion problems based on adaptive Chebyshev's smoothers
\jour Matem. Mod.
\yr 2014
\vol 26
\issue 9
\pages 126--140
\mathnet{http://mi.mathnet.ru/mm3520}
\transl
\jour Math. Models Comput. Simul.
\yr 2015
\vol 7
\issue 2
\pages 117--127
\crossref{https://doi.org/10.1134/S2070048215020118}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84929073855}


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    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. Zhukov V.T., Krasnov M.M., Novikova N.D., Feodoritova O.B., “Multigrid Effectiveness on Modern Computing Architectures”, Program. Comput. Softw., 41:1 (2015), 14–22  crossref  isi  elib  scopus
    2. V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “Multigrid method for elliptic equations with anisotropic discontinuous coefficients”, Comput. Math. Math. Phys., 55:7 (2015), 1150–1163  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. 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
    4. 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
    5. 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
    6. V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “Adaptivnyi chebyshevskii iteratsionnyi metod”, Matem. modelirovanie, 30:10 (2018), 67–85  mathnet
    7. V. T. Zhukov, V. M. Krasnov, M. M. Krasnov, N. D. Novikova, O. B. Feodoritova, “O chislennoi modeli fizicheskikh protsessov v vysokotemperaturnykh sverkhprovodnikakh”, Preprinty IPM im. M. V. Keldysha, 2019, 129, 21 pp.  mathnet  crossref
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