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Particle Based gPC Methods for Mean-Field Models of Swarming with Uncertainty

Particle Based gPC Methods for Mean-Field Models of Swarming with Uncertainty
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Year:    2019

Communications in Computational Physics, Vol. 25 (2019), Iss. 2 : pp. 508–531

Abstract

In this work we focus on the construction of numerical schemes for the approximation of stochastic mean-field equations which preserve the nonnegativity of the solution. The method here developed makes use of a mean-field Monte Carlo method in the physical variables combined with a generalized Polynomial Chaos (gPC) expansion in the random space. In contrast to a direct application of stochastic-Galerkin methods, which are highly accurate but lead to the loss of positivity, the proposed schemes are capable to achieve high accuracy in the random space without loosing nonnegativity of the solution. Several applications of the schemes to mean-field models of collective behavior are reported.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2017-0244

Communications in Computational Physics, Vol. 25 (2019), Iss. 2 : pp. 508–531

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Uncertainty quantification stochastic Galerkin mean-field equations swarming dynamics.

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