TY - JOUR
T1 - Particle Based gPC Methods for Mean-Field Models of Swarming with Uncertainty
JO - Communications in Computational Physics
VL - 2
SP - 508
EP - 531
PY - 2018
DA - 2018/10
SN - 25
DO - http://doi.org/10.4208/cicp.OA-2017-0244
UR - https://global-sci.org/intro/article_detail/cicp/12761.html
KW - Uncertainty quantification, stochastic Galerkin, mean-field equations, swarming dynamics.
AB - <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>