"Tensor decompositions for solving the equations of mathematical models of aggregation with multiple collisions of particles"
Stefonishin D.A., Matveev S.A., Smirnov A.P., and Tyrtyshnikov E.E.

Efficient methods for the numerical solving of a Cauchy problem for systems of Smoluchowski-type kinetic equations of aggregation with multiple collisions of particles are proposed. The developed methods are based on the tensor representations of kinetic coefficient arrays. The canonical, Tucker, and tensor train (TT) decompositions are compared. The computational complexity of these tensor representations is estimated for a second-order Runge-Kutta. The efficiency of the proposed methods for the systems with collisions of up to five particles is shown in a series of numerical experiments for the canonical and TT-decompositions.

Keywords: multiple collision 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