Efficient numerical calculation of drift and diffusion coefficients in the diffusion approximation of kinetic equations

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Title: Efficient numerical calculation of drift and diffusion coefficients in the diffusion approximation of kinetic equations
Author(s): Bonaille-Noel, V
Carrillo de la Plata, J
Goudon, T
Pavlotis, G
Item Type: Journal Article
Abstract: In this paper we study the diffusion approximation of a swarming model given by a system of interacting Langevin equations with nonlinear friction. The diffusion approximation requires the calculation of the drift and diffusion coefficients that are given as averages of solutions to appropriate Poisson equations. We present a new numerical method for computing these coefficients that is based on the calculation of the eigenvalues and eigenfunctions of a Schr¨odinger operator. These theoretical results are supported by numerical simulations showcasing the efficiency of the method.
Publication Date: 4-Mar-2016
Date of Acceptance: 30-Nov-2015
URI: http://hdl.handle.net/10044/1/29000
DOI: https://dx.doi.org/10.1093/imanum/drv066
ISSN: 0272-4979
Publisher: Oxford University Press
Start Page: 1536
End Page: 1569
Journal / Book Title: IMA Journal of Numerical Analysis
Volume: 36
Issue: 4
Copyright Statement: © The authors 2016. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Royal Society
Engineering & Physical Science Research Council (E
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/J009636/1
WM120001
EP/K008404/1
EP/L025159/1
EP/L020564/1
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
diffusion approximation
eigenvalue problem
Schrodinger operators
FOKKER-PLANCK SYSTEM
POISSON-EQUATION
PERIODIC POTENTIALS
LIMIT
TRANSPORT
HOMOGENIZATION
DYNAMICS
PARTICLE
FIELD
COMPUTATIONS
Numerical & Computational Mathematics
0102 Applied Mathematics
0103 Numerical And Computational Mathematics
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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