Groupe d’études et de recherche en analyse des décisions

Quasi-Monte Carlo simulation of coagulation and fragmentation

Christian Lécot CNRS, LAMA, Université de Savoie, France

Coagulation and fragmentation models have applications in many domains of science, technology and engineering: aerosol dynamics, nanoparticle generation, crystallization, precipitation, granulation, polymerization, combustion processes, food processes, pollutant formation in flames, microbial systems.

The Monte Carlo method is a powerful tool for solving many problems in the applied sciences. This is a simple, versatile, and robust method but it may suffer from a lack of precision. We explore the quasi-Monte Carlo (QMC) way to improve the accuracy of Monte Carlo simulations of coagulation and fragmentation by replacing the pseudo-random numbers with low discrepancy point sets; the present work extends the method analyzed in [1].

The mass distribution is approximated by a finite number N of numerical particles. Time is discretized and quasi-random points are used at every time step to determine whether each particle is undergoing a coagulation or a fragmentation. In addition, the particles are relabeled according to their increasing mass at each time step. Convergence of the schemes is analyzed when N goes to infinity. Numerical tests show that the computed solutions are in good agreement with analytical ones, when available, and the QMC algorithm reduces the discrepancy of the standard Monte Carlo approach.

[1] C. Lécot and A. Tarhini. A quasi-Monte Carlo method for the coagulation equation. In G. Larcher, F. Pillichshammer, A. Winterhof, and C. Xing, editors, Applied Algebra and Number Theory, pages 216-234. Cambridge University Press, Cambridge, 2014.


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