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Stochastic particle methods for Smoluchowski coagulation equation: variance reduction and error estimations

Author

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  • Kolodko A.

    (1. Institute of Comput. Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Lavrentieva str., 6, 630090 Novosibirsk, Russia)

  • Sabelfeld K.

    (1. Institute of Comput. Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Lavrentieva str., 6, 630090 Novosibirsk, Russia)

Abstract

Stochastic particle methods for the coagulation-fragmentation Smoluchowski equation are developed and a general variance reduction technique is suggested. This method generalizes the mass-flow approach due to H. Babovski, and has in focus the desired band of the size spectrum. Estimations of the variance and bias of the method are derived. A comparative cost and variance analysis is made for the known stochastic methods. An applied problem of coagulation-evaporation dynamics in free molecule regime is solved.

Suggested Citation

  • Kolodko A. & Sabelfeld K., 2003. "Stochastic particle methods for Smoluchowski coagulation equation: variance reduction and error estimations," Monte Carlo Methods and Applications, De Gruyter, vol. 9(4), pages 315-339, December.
    • Handle: RePEc:bpj:mcmeap:v:9:y:2003:i:4:p:315-339:n:3
    DOI: 10.1515/156939603322601950
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    References listed on IDEAS

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    1. Sabelfeld K.K. & Rogasinsky S.V. & Kolodko A.A. & Levykin A.I., 1996. "Stochastic algorithms for solving Smolouchovsky coagulation equation and applications to aerosol growth simulation," Monte Carlo Methods and Applications, De Gruyter, vol. 2(1), pages 41-88, December.
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    Cited by:

    1. Lécot C. & Tarhini A., 2008. "A quasi-stochastic simulation of the general dynamics equation for aerosols," Monte Carlo Methods and Applications, De Gruyter, vol. 13(5-6), pages 369-388, January.
    2. Wells Clive G. & Kraft Markus, 2005. "Direct Simulation and Mass Flow Stochastic Algorithms to Solve a Sintering-Coagulation Equation," Monte Carlo Methods and Applications, De Gruyter, vol. 11(2), pages 175-197, June.
    3. Sabelfeld Karl K. & Eremeev Georgy, 2018. "A hybrid kinetic-thermodynamic Monte Carlo model for simulation of homogeneous burst nucleation," Monte Carlo Methods and Applications, De Gruyter, vol. 24(3), pages 193-202, September.

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    13. Sabelfeld, Karl & Kolodko, Anastasia, 2003. "Stochastic Lagrangian models and algorithms for spatially inhomogeneous Smoluchowski equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(2), pages 115-137.

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