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Keldysh Institute preprints, 2016, 113, 32 pages (Mi ipmp2187)  

This article is cited in 2 scientific papers (total in 2 papers)

Algebraic multigrid method with adaptive smoothers based on Chebyshev polynomials

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


Abstract: We introduce an adaptive algebraic multigrid method (AMG) for numerical solution of three-dimensional elliptic equations. A new element is the integration of AMG technique with the smoothers based on optimal Chebyshev polynomials. The possibilities of automatic adaptation of smoothers to the bounds of the АMG discrete operators are shown. The properties of two smoothers, the polynomial and the rational function, are discussed. The results of experimental verification of the AMG are given. Effective implementation of the smoothers and solver for the coarsest equations with the help of Chebyshev explicit-iterative algorithms enables the functioning of the parallel code on modern supercomputer architectures.

Keywords: elliptic equations, algebraic multigrid method, Chebyshev polynomials, adaptive smoother.

Funding Agency Grant Number
Russian Science Foundation 14-21-00025


DOI: https://doi.org/10.20948/prepr-2016-113

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Document Type: Preprint

Citation: V. T. Zhukov, M. M. Krasnov, N. D. Novikova, O. B. Feodoritova, “Algebraic multigrid method with adaptive smoothers based on Chebyshev polynomials”, Keldysh Institute preprints, 2016, 113, 32 pp.

Citation in format AMSBIB
\Bibitem{ZhuKraNov16}
\by V.~T.~Zhukov, M.~M.~Krasnov, N.~D.~Novikova, O.~B.~Feodoritova
\paper Algebraic multigrid method with adaptive smoothers based on Chebyshev polynomials
\jour Keldysh Institute preprints
\yr 2016
\papernumber 113
\totalpages 32
\mathnet{http://mi.mathnet.ru/ipmp2187}
\crossref{https://doi.org/10.20948/prepr-2016-113}


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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, “Chebyshevskie iteratsii s adaptivnym utochneniem nizhnei granitsy spektra matritsy”, Preprinty IPM im. M. V. Keldysha, 2018, 172, 32 pp.  mathnet  crossref
    2. V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “Adaptivnyi chebyshevskii iteratsionnyi metod”, Matem. modelirovanie, 30:10 (2018), 67–85  mathnet
  • Препринты Института прикладной математики им. М. В. Келдыша РАН
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