Numerical studies of solutions for kinetic equations with many-particle collisions

S. A. Matveev, D. A. Stefonishin, A. P. Smirnov, A. A. Sorokin, E. E. Tyrtyshnikov

    Research output: Contribution to journalConference articlepeer-review

    2 Citations (Scopus)


    In this work we present a method of low-rank tensor decompositions to accelerate evaluation of the right-hand side of systems of kinetic equations with many-particle collisional terms. These equations can be interpreted as a generalization of classical Smoluchowski aggregation equations allowing one to consider not only binary collisions of particles but also triple collisions. Straight-forward evaluation of the right-hand side for such system of N equations with k = 1, 2,..., N requires O(N 3) numerical operations and we find such complexity too high for practical investigations. However, under assumptions that kinetic coefficients can be represented with either canonical polyadic (CP) or tensor train decomposition (TT) with the rank R ≪ N we can propose algorithms evaluating the right-hand side with much lower complexities: O(NRlog N) and O(NR 2 log N) for CP and TT respectively. We compare numerical solutions with different triple-collision rates and obtain a significant influence of accounting triple collisional effects.

    Original languageEnglish
    Article number012008
    JournalJournal of Physics: Conference Series
    Issue number1
    Publication statusPublished - 26 Mar 2019
    Event3rd International Conference on Computer Simulations in Physics and Beyond, CSP 2018 - Moscow, Russian Federation
    Duration: 24 Sep 201827 Sep 2018


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