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Matem. Mod., 2014, Volume 26, Number 1, Pages 55–68 (Mi mm3438)  

This article is cited in 10 scientific papers (total in 10 papers)

Parallel multigrid method for solving elliptic equations

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

Keldysh Institute of Applied Mathematics

Abstract: Proposed algorithm represents an efficient parallel implementation of the multigrid method of R. P. Fedorenko and is intended for solving three-dimensional elliptic equations. Scalability is provided by the usage of the Chebyshev iteration for solution of the coarsest grid equations and for construction of the smoothing procedures. The calculation results are given; they confirm the efficiency of the algorithm and scalability of the parallel code.

Keywords: numerical simulation, three-dimensional elliptic equations, multigrid, Chebyshev iteration, parallel implementation.

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English version:
Mathematical Models and Computer Simulations, 2014, 6:4, 425–434

Document Type: Article
UDC: 519.6
Received: 11.02.2013

Citation: V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “Parallel multigrid method for solving elliptic equations”, Matem. Mod., 26:1 (2014), 55–68; Math. Models Comput. Simul., 6:4 (2014), 425–434

Citation in format AMSBIB
\by V.~T.~Zhukov, N.~D.~Novikova, O.~B.~Feodoritova
\paper Parallel multigrid method for solving elliptic equations
\jour Matem. Mod.
\yr 2014
\vol 26
\issue 1
\pages 55--68
\jour Math. Models Comput. Simul.
\yr 2014
\vol 6
\issue 4
\pages 425--434

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    This publication is cited in the following articles:
    1. V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “O mnogosetochnom i yavno-iteratsionnom metodakh resheniya parabolicheskikh uravnenii”, Preprinty IPM im. M. V. Keldysha, 2014, 028, 36 pp.  mathnet
    2. V. T. Zhukov, M. M. Krasnov, N. D. Novikova, O. B. Feodoritova, “Parallelnyi mnogosetochnyi metod: sravnenie effektivnosti na sovremennykh vychislitelnykh arkhitekturakh”, Preprinty IPM im. M. V. Keldysha, 2014, 031, 22 pp.  mathnet
    3. V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “Multigrid for anisotropic diffusion problems based on adaptive Chebyshev's smoothers”, Math. Models Comput. Simul., 7:2 (2015), 117–127  mathnet  crossref
    4. V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “O primenenii mnogosetochnogo i yavno-iteratsionnogo metodov k resheniyu parabolicheskikh uravnenii s anizotropnymi razryvnymi koeffitsientami”, Preprinty IPM im. M. V. Keldysha, 2014, 085, 24 pp.  mathnet
    5. 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
    6. 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
    7. 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
    8. A. Gorobets, “On technology of large-scale CFD simulations”, Math. Models Comput. Simul., 8:6 (2016), 660–670  mathnet  crossref  elib
    9. 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
    10. J. Li, Zh. Zheng, Q. Tian, G. Zhang, F. Zheng, Yu. Pan, “Research on tridiagonal matrix solver design based on a combination of processors”, Comput. Electr. Eng., 62 (2017), 1–16  crossref  isi  scopus
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