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

Thierry Goudon 1, 2 Virginie Bonnaillie-Noël 3 José Antonio Carrillo 4 Pavliotis Greg 4
1 JAD - Laboratoire Jean Alexandre Dieudonné
2 COFFEE - COmplex Flows For Energy and Environment
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
3 DMA - Département de Mathématiques et Applications - ENS Paris
4 Department of Mathematics [Imperial College London]
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 Schrodinger operator. These theoretical results are supported by numerical simulations showcasing the efficiency of the method.
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https://hal.inria.fr/hal-01270345
Contributor : Thierry Goudon Connect in order to contact the contributor
Submitted on : Sunday, February 7, 2016 - 1:12:37 AM
Last modification on : Tuesday, January 18, 2022 - 2:26:05 PM

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  • HAL Id : hal-01270345, version 1

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Citation

Thierry Goudon, Virginie Bonnaillie-Noël, José Antonio Carrillo, Pavliotis Greg. Efficient numerical calculation of drift and diffusion coefficients for the diffusion approximation of kinetic equations. IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2016. ⟨hal-01270345⟩

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