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Low-rank Monte Carlo method for aggregation kinetics with particle sources

  • Sergey Matveev EMAIL logo and Roman Dyachenko
Published/Copyright: August 1, 2025

Abstract

In this work we propose an extension of the low-rank Monte Carlo algorithm for modelling aggregation process with multiple sources of particles. This implementation utilizes the low-rank structure of the coagulation kernel and reduces the number of operations for selection of pairs of coagulating particles. This approach does not require the kernel itself to be low-rank or to have such an approximation. Instead, it is sufficient to use an auxiliary low-rank kernel as a majorant function. We demonstrate the convergence of our method using the known theoretical solutions and show an agreement of the numerical particle size distributions with the results obtained by the deterministic numerical method. In addition, we analyze the performance of the Monte Carlo method for a simplified system with active monomers and collisional shattering events. We remind that numerical modelling based on relatively small number of finite samples can deviate from analytical solution of the kinetic equations.

MSC 2010: 15A23; 15B48; 65F30; 65Y20; 68W20

Funding statement: This work was supported by the Russian Science Foundation project 25-21-00047.

Acknowledgment

Sergey Matveev is grateful to prof. Valery Zagaynov for useful discussions that provoked us to prepare this manuscript.

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Received: 2025-04-03
Revised: 2025-06-12
Accepted: 2025-06-16
Published Online: 2025-08-01
Published in Print: 2025-08-26

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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