@Article{CiCP-25-508,
author = {José Antonio Carrillo, Lorenzo Pareschi and Mattia Zanella},
title = {Particle Based gPC Methods for Mean-Field Models of Swarming with Uncertainty},
journal = {Communications in Computational Physics},
year = {2018},
volume = {25},
number = {2},
pages = {508--531},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0244},
url = {http://global-sci.org/intro/article_detail/cicp/12761.html}
}