DOI: https://doi.org/10.26089/NumMet.v19r325

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

Authors

  • D.A. Stefonishin
  • S.A. Matveev
  • A.P. Smirnov
  • E.E. Tyrtyshnikov

Keywords:

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

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(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.

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Published

2018-12-26

Issue

Vol. 19 (2018): Issue 3.

Section

Section 1. Numerical methods and applications

Author Biographies

D.A. Stefonishin

Lomonosov Moscow State University
• PhD Student

S.A. Matveev

Skolkovo Institute of Science and Technology
• Junior Researcher

A.P. Smirnov

Lomonosov Moscow State University
• Associate Professor

E.E. Tyrtyshnikov

Institute of Numerical Mathematics of RAS (INM RAS)
• Director

References

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