Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et Analyse

Collection Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et Analyse

Organizer(s) Bostan, Mihaï ; Jin, Shi ; Mehrenberger, Michel ; Montibeller, Celine

Date(s) 22/03/2021 - 26/03/2021

linked URL https://www.chairejeanmorlet.com/2355.html

00:00:00 / 00:00:00

17 19

An asymptotic preserving method for Levy Fokker Planck equation with fractional diffusion limit

We develop a numerical method for the Levy-Fokker-Planck equation with the fractional diffusive scaling. There are two main challenges. One comes from a two-fold non locality, that is, the need to apply the fractional Laplacian operator to a power law decay distribution. The other comes from long-time/small mean-free-path scaling, which calls for a uniform stable solver. To resolve the first difficulty, we use a change of variable to convert the unbounded domain into a bounded one and then apply Chebyshev polynomial based pseudo-spectral method. To resolve the second issue, we propose an asymptotic preserving scheme based on a novel micro-macro decomposition that uses the structure of the test function in proving the fractional diffusion limit analytically.

Information about the video

Date of recording 23/03/2021
Date of publication 09/04/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19735603
Cite this video Wang, Li (23/03/2021). An asymptotic preserving method for Levy Fokker Planck equation with fractional diffusion limit. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19735603
URL https://dx.doi.org/10.24350/CIRM.V.19735603

Domain(s)

Numerical Analysis

Bibliography

XU, Wuzhe et WANG, Li. An asymptotic preserving scheme for L\'{e} vy-Fokker-Planck equation with fractional diffusion limit. arXiv preprint arXiv:2103.08848, 2021. - https://arxiv.org/abs/2103.08848

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Li_WANG.pdf

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