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.
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.
\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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This publication is cited in the following 4 articles:
A P Karpov, V A Erzunov, E B Shchanikova, Yu G Bartenev, “Adaptive preconditioning for a stream of SLAEs”, J. Phys.: Conf. Ser., 2099:1 (2021), 012008
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.
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.
V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “An adaptive Chebyshev iterative method”, Math. Models Comput. Simul., 11:3 (2019), 426–437
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