"An efficient finite-difference method for solving Smoluchowski-type kinetic equations of aggregation with three-body collisions"
Stefonishin D.A., Matveev S.A., Smirnov A.P., and Tyrtyshnikov E.E.

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(N3) of the finite-difference predictor-corrector scheme to O(RNlogN) 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.

  • Stefonishin D.A. – Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics; Leninskie Gory, Moscow, 119992, Russia; Graduate Student, e-mail: stefonishin@gmail.com
  • Matveev S.A. – Skolkovo Institute of Science and Technology; ulitsa Nobelya, 3, Skolkovo Innovation Center, Moscow Region, 121205, Russia; Ph.D., Junior Scientist, e-mail: s.matveev@skoltech.ru
  • Smirnov A.P. – Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics; Leninskie Gory, Moscow, 119992, Russia; Ph.D., Associate Professor, e-mail: sap@cs.msu.su
  • Tyrtyshnikov E.E. – Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences; ulitsa Gubkina 8, Moscow, 119333, Russia; Dr. Sci., Professor, Academician of Russian Academy of Sciences, Director, e-mail: eugene.tyrtyshnikov@gmail.com