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Vychisl. Metody Programm., 2018, Volume 19, Issue 3, Pages 261–269 (Mi vmp918)  

An efficient finite-difference method for solving Smoluchowski-type kinetic equations of aggregation with three-body collisions

D. A. Stefonishina, S. A. Matveevb, A. P. Smirnova, E. E. Tyrtyshnikovc

a Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
b Skolkovo Institute of Science and Technology
c Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow

Abstract: We consider a model of aggregation processes for the Smoluchowski-type kinetic equations with three-body collisions of particles. We propose a numerical method for the fast solving of Cauchy problems for the corresponding systems of equations. The proposed method allows one to reduce the step complexity $O (N^{3})$ of the finite-difference predictor-corrector scheme to $O (RN\log N)$ without loss of accuracy. Here the parameter $N$ specifies the number of considered equations and $R$ is the rank of kinetic coefficient arrays. The efficiency and accuracy of the proposed numerical method are demonstrated for model problems of aggregation kinetics.

Keywords: three-body Smoluchowski equation, kinetics of aggregation processes, predictor-corrector scheme, low-rank tensor approximations, discrete convolution

Full text: PDF file (335 kB)

UDC: 519.6
Received: 30.04.2018

Citation: D. A. Stefonishin, S. A. Matveev, A. P. Smirnov, E. E. Tyrtyshnikov, “An efficient finite-difference method for solving Smoluchowski-type kinetic equations of aggregation with three-body collisions”, Vychisl. Metody Programm., 19:3 (2018), 261–269

Citation in format AMSBIB
\Bibitem{SteMatSmi18}
\by D.~A.~Stefonishin, S.~A.~Matveev, A.~P.~Smirnov, E.~E.~Tyrtyshnikov
\paper An efficient finite-difference method for solving Smoluchowski-type kinetic equations of aggregation with three-body collisions
\jour Vychisl. Metody Programm.
\yr 2018
\vol 19
\issue 3
\pages 261--269
\mathnet{http://mi.mathnet.ru/vmp918}


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