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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 8, Pages 1305–1319 (Mi zvmmf10246)  

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

On the solution of evolution equations based on multigrid and explicit iterative methods

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: Two schemes for solving initial–boundary value problems for three-dimensional parabolic equations are studied. One is implicit and is solved using the multigrid method, while the other is explicit iterative and is based on optimal properties of the Chebyshev polynomials. In the explicit iterative scheme, the number of iteration steps and the iteration parameters are chosen as based on the approximation and stability conditions, rather than on the optimization of iteration convergence to the solution of the implicit scheme. The features of the multigrid scheme include the implementation of the intergrid transfer operators for the case of discontinuous coefficients in the equation and the adaptation of the smoothing procedure to the spectrum of the difference operators. The results produced by these schemes as applied to model problems with anisotropic discontinuous coefficients are compared.

Key words: three-dimensional parabolic equations, anisotropic discontinuous coefficients, multigrid method, explicit iterative scheme with Chebyshev parameters.

DOI: https://doi.org/10.7868/S0044466915080177

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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:8, 1276–1289

Bibliographic databases:

UDC: 519.63
Received: 26.02.2015

Citation: V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “On the solution of evolution equations based on multigrid and explicit iterative methods”, Zh. Vychisl. Mat. Mat. Fiz., 55:8 (2015), 1305–1319; Comput. Math. Math. Phys., 55:8 (2015), 1276–1289

Citation in format AMSBIB
\by V.~T.~Zhukov, N.~D.~Novikova, O.~B.~Feodoritova
\paper On the solution of evolution equations based on multigrid and explicit iterative methods
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2015
\vol 55
\issue 8
\pages 1305--1319
\jour Comput. Math. Math. Phys.
\yr 2015
\vol 55
\issue 8
\pages 1276--1289

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    This publication is cited in the following articles:
    1. V. T. Zhukov, M. M. Krasnov, N. D. Novikova, O. B. Feodoritova, “Chislennoe reshenie parabolicheskikh uravnenii na lokalno-adaptivnykh setkakh chebyshevskim metodom”, Preprinty IPM im. M. V. Keldysha, 2015, 087, 26 pp.  mathnet
    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
    6. V. T. Zhukov, O. B. Feodoritova, “O razvitii parallelnykh algoritmov resheniya parabolicheskikh i ellipticheskikh uravnenii”, Matematicheskii analiz, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 155, VINITI RAN, M., 2018, 20–37  mathnet  mathscinet
    7. 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
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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