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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 12, Pages 2110–2121 (Mi zvmmf215)  
This article is cited in 3 scientific papers (total in 3 papers)

Modifications of weighted Monte Carlo algorithms for nonlinear kinetic equations

M. A. Korotchenko, G. A. Mikhailov, S. V. Rogazinskii

Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, pr. Akademika Lavrent'eva 6, 630090, Russia
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Abstract: Test problems for the nonlinear Boltzmann and Smoluchowski kinetic equations are used to analyze the efficiency of various versions of weighted importance modeling as applied to the evolution of multiparticle ensembles. For coagulation problems, a considerable gain in computational costs is achieved via the approximate importance modeling of the “free path” of the ensemble combined with the importance modeling of the index of a pair of interacting particles. A weighted modification of the modeling of the initial velocity distribution was found to be the most efficient for model solutions to the Boltzmann equation. The technique developed can be useful as applied to real-life coagulation and relaxation problems for which the model problems considered give approximate solutions.
Key words: weighted Monte Carlo algorithms, solution to nonlinear Boltzmann and Smoluchowski kinetic equations.
Received: 22.05.2007
English version:
Computational Mathematics and Mathematical Physics, 2007, Volume 47, Issue 12, Pages 2023–2033
DOI: https://doi.org/10.1134/S0965542507120123
Bibliographic databases:
Document Type: Article
UDC: 519.676
Language: Russian
Citation: M. A. Korotchenko, G. A. Mikhailov, S. V. Rogazinskii, “Modifications of weighted Monte Carlo algorithms for nonlinear kinetic equations”, Zh. Vychisl. Mat. Mat. Fiz., 47:12 (2007), 2110–2121; Comput. Math. Math. Phys., 47:12 (2007), 2023–2033
Citation in format AMSBIB
\Bibitem{KorMikRog07}
\by M.~A.~Korotchenko, G.~A.~Mikhailov, S.~V.~Rogazinskii
\paper Modifications of weighted Monte Carlo algorithms for nonlinear kinetic equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 12
\pages 2110--2121
\mathnet{http://mi.mathnet.ru/zvmmf215}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2394968}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 12
\pages 2023--2033
\crossref{https://doi.org/10.1134/S0965542507120123}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-37649010477}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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