Particle based gPC methods for mean-field models of swarming with uncertainty

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Title: Particle based gPC methods for mean-field models of swarming with uncertainty
Authors: Carrillo de la Plata, J
Pareschi, L
Zanella, M
Item Type: Journal Article
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.
Issue Date: 1-Jan-2019
Date of Acceptance: 27-Mar-2018
URI: http://hdl.handle.net/10044/1/58621
DOI: https://dx.doi.org/10.4208/cicp.OA-2017-0244
ISSN: 1815-2406
Publisher: Global Science Press
Start Page: 508
End Page: 531
Journal / Book Title: Communications in Computational Physics
Volume: 25
Issue: 2
Copyright Statement: © 2019 Global-Science Press.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/P031587/1
Keywords: Applied Mathematics
Publication Status: Published
Online Publication Date: 2018-10-01
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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