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Tensorisation in the Solution of Smoluchowski Type Equations

  • Ivan TimokhinEmail author
Conference paper
  • 9 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11958)

Abstract

We investigate the structure of the non-linear operator featured in the Smoluchowski-type system of ordinary differential equations, and find a way to express it algebraically in terms of the parameters of the problem and a few auxiliary tensors, describing, in a sense, the “shape” of the system. We find compact representations of these auxiliary tensors in terms of a Tensor Train decomposition. Provided the parameters admit a compact representation in this format as well, this allows us to rather straightforwardly reuse standard numerical algorithms for a wide range of associated problems, obtaining \(O(\log N)\) asymptotic complexity.

Notes

Acknowledgements

The work was supported by the Russian Science Foundation, grant 19-11-00338.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Computational Mathematics and CyberneticsLomonosov Moscow State UniversityMoscowRussia
  2. 2.Marchuk Institute of Numerical MathematicsRussian Academy of SciencesMoscowRussia

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