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Monte Carlo stochastic Galerkin methods for non-Maxwellian kinetic models of multiagent systems with uncertainties

Author

Listed:
  • Andrea Medaglia

    (University of Pavia)

  • Andrea Tosin

    (Politecnico di Torino)

  • Mattia Zanella

    (University of Pavia)

Abstract

In this paper, we focus on the construction of a hybrid scheme for the approximation of non-Maxwellian kinetic models with uncertainties. In the context of multiagent systems, the introduction of a kernel at the kinetic level is useful to avoid unphysical interactions. The methods here proposed, combine a direct simulation Monte Carlo (DSMC) in the phase space together with stochastic Galerkin (sG) methods in the random space. The developed schemes preserve the main physical properties of the solution together with accuracy in the random space. The consistency of the methods is tested with respect to surrogate Fokker–Planck models that can be obtained in the quasi-invariant regime of parameters. Several applications of the schemes to non-Maxwellian models of multiagent systems are reported.

Suggested Citation

  • Andrea Medaglia & Andrea Tosin & Mattia Zanella, 2022. "Monte Carlo stochastic Galerkin methods for non-Maxwellian kinetic models of multiagent systems with uncertainties," Partial Differential Equations and Applications, Springer, vol. 3(4), pages 1-30, August.
    • Handle: RePEc:spr:pardea:v:3:y:2022:i:4:d:10.1007_s42985-022-00189-w
    DOI: 10.1007/s42985-022-00189-w
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    References listed on IDEAS

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    1. Federico Bassetti & Giuseppe Toscani, 2010. "Explicit equilibria in a kinetic model of gambling," Papers 1002.3689, arXiv.org.
    2. Adrian Dragulescu & Victor M. Yakovenko, 2000. "Statistical mechanics of money," Papers cond-mat/0001432, arXiv.org, revised Aug 2000.
    3. Zanella, Mattia, 2020. "Structure preserving stochastic Galerkin methods for Fokker–Planck equations with background interactions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 168(C), pages 28-47.
    4. Pareschi, Lorenzo & Toscani, Giuseppe, 2013. "Interacting Multiagent Systems: Kinetic equations and Monte Carlo methods," OUP Catalogue, Oxford University Press, number 9780199655465.
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