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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 2, Pages 298–317
DOI: https://doi.org/10.7868/S0044466914020082 (Mi zvmmf9993) 		 
This article is cited in 10 scientific papers (total in 10 papers)

New two-level leapfrog scheme for modeling the stochastic Landau–Lifshitz equations

V. Yu. Glotova, V. M. Goloviznina, S. A. Karabasovb, A. P. Markeshteijnb

a Nuclear Safety Institute, Russian Academy of Sciences, Bol’shaya Tul’skaya ul. 52, Moscow, 115191, Russia
b School of Engineering and Materials Science, Queen Mary, University of London, Mule End Road, London, E1 4NS, UK
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DOI: https://doi.org/10.7868/S0044466914020082
Abstract: A two-level modification of the classical nondissipative leapfrog scheme with nonlinear flux correction has been developed for fluctuating hydrodynamics problems. The new algorithm has shown to satisfy the fluctuation-dissipation theorem to high accuracy. The results of various numerical tests, including equilibrium, nonequilibrium, one-, and two-dimensional systems, are compared with theoretical predictions, direct molecular simulations, and results produced by MacCormack’s schemes, the piecewise parabolic method, and a third-order Runge–Kutta scheme. The new algorithm is well suited for parallel computations due to its implementation simplicity and compact stencil.
Key words: stochastic Landau–Lifshitz equations, fluctuating hydrodynamics, multiscale problems, leapfrog scheme.
Received: 06.05.2013
Revised: 28.08.2013
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 2, Pages 315–334
DOI: https://doi.org/10.1134/S0965542514020079
Bibliographic databases:
Document Type: Article
UDC: 519.676
Language: Russian
Citation: V. Yu. Glotov, V. M. Goloviznin, S. A. Karabasov, A. P. Markeshteijn, “New two-level leapfrog scheme for modeling the stochastic Landau–Lifshitz equations”, Zh. Vychisl. Mat. Mat. Fiz., 54:2 (2014), 298–317; Comput. Math. Math. Phys., 54:2 (2014), 315–334
Citation in format AMSBIB
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    • This publication is cited in the following 10 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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