English
An asymptotic preserving method for Levy Fokker Planck equation with fractional diffusion limit
Virtualconference
Auteurs : Wang, Li (Auteur de la Conférence)
CIRM (Editeur )
45K05 - Integro-partial differential equations
65M70 - Spectral, collocation and related methods
82C40 - Kinetic theory of gases
82C80 - Numerical methods (Monte Carlo, series resummation, etc.)
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Li_WANG.pdf
CIRM (Editeur )
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Résumé :
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.
Codes MSC : 45K05 - Integro-partial differential equations
65M70 - Spectral, collocation and related methods
82C40 - Kinetic theory of gases
82C80 - Numerical methods (Monte Carlo, series resummation, etc.)
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Li_WANG.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 09/04/2021 Date de captation : 23/03/2021 Sous collection : Research talks arXiv category : Numerical Analysis Domaine : Numerical Analysis & Scientific Computing Format : MP4 (.mp4) - HD Durée : 00:32:23 Audience : Researchers Download : https://videos.cirm-math.fr/2021-03-23_Wang.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et AnalyseOrganisateurs de la rencontre : Bostan, Mihaï ; Jin, Shi ; Mehrenberger, Michel ; Montibeller, Celine Dates : 22/03/2021 - 26/03/2021 Année de la rencontre : 2021 URL Congrès : https://www.chairejeanmorlet.com/2355.html
Données de citation
DOI : 10.24350/CIRM.V.19735603Citer cette vidéo: Wang, Li (2021). An asymptotic preserving method for Levy Fokker Planck equation with fractional diffusion limit. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19735603 URI : http://dx.doi.org/10.24350/CIRM.V.19735603 |
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Bibliographie
- 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
