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.
Citation:
V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “Parallel multigrid method for solving elliptic equations”, Mat. Model., 26:1 (2014), 55–68; Math. Models Comput. Simul., 6:4 (2014), 425–434
This publication is cited in the following 18 articles:
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O B Feodoritova, V T Zhukov, “An adaptive multigrid on block-structured grids”, J. Phys.: Conf. Ser., 1640:1 (2020), 012020
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.
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O B Feodoritova, M M Krasnov, V T Zhukov, “Adaptive technique for Chebyshev-Based solvers for three-dimensional elliptic equations”, J. Phys.: Conf. Ser., 1103 (2018), 012012
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
A. Gorobets, “On technology of large-scale CFD simulations”, Math. Models Comput. Simul., 8:6 (2016), 660–670
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.
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
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
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
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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.
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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.
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