CIRM - Videos & books Library - A new stability and convergence proof of the Fourier-Galerkin spectral method for the spatially homogeneous Boltzmann equation

Virtualconference

Auteurs : Hu, Jingwei (Auteur de la conférence)
CIRM (Editeur )

Loading the player...

Résumé : Numerical approximation of the Boltzmann equation is a challenging problem due to its high-dimensional, nonlocal, and nonlinear collision integral. Over the past decade, the Fourier-Galerkin spectral method has become a popular deterministic method for solving the Boltzmann equation, manifested by its high accuracy and potential of being further accelerated by the fast Fourier transform. Albeit its practical success, the stability of the method is only recently proved by Filbet, F. & Mouhot, C. in [Trans.Amer.Math.Soc. 363, no. 4 (2011): 1947-1980.] by utilizing the”spreading” property of the collision operator. In this work, we provide anew proof based on a careful L2 estimate of the negative part of the solution. We also discuss the applicability of the result to various initial data, including both continuous and discontinuous functions. This is joint work with Kunlun Qi and Tong Yang.

Mots-Clés : Boltzmann equation; Fourier-Galerkin spectral method; well-posedness; stability; convergence; discontinuous; filter

Codes MSC :
35Q20 - Boltzmann equations
45G10 - Other nonlinear integral equations
65M12 - Stability and convergence of numerical methods (IVP of PDE)
65M70 - Spectral, collocation and related methods

Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2355/Slides/slide_Jingwei_HU.pdf

Informations sur la Vidéo

Réalisateur :

Hennenfent, Guillaume

Langue :

Date de Publication :

Date de Captation :

Sous Collection :

Catégorie arXiv :

Domaine(s) :

Format :

Durée :

Audience :

Download :

https://videos.cirm-math.fr/2021-03-22_Hu.mp4

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 Analyse
Organisateurs de la Rencontre : Bostan, Mihaï ; Jin, Shi ; Mehrenberger, Michel ; Montibeller, Celine
Dates : 22/03/2021 - 26/03/2021
Année de la rencontre : 2021
URL de la Rencontre : https://www.chairejeanmorlet.com/2355.html

Données de citation

DOI : 10.24350/CIRM.V.19734303
Citer cette vidéo: Hu, Jingwei (2021). A new stability and convergence proof of the Fourier-Galerkin spectral method for the spatially homogeneous Boltzmann equation. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19734303
URI : http://dx.doi.org/10.24350/CIRM.V.19734303

Voir Aussi

[Virtualconference] Model predictive and random batch methods for a guiding problem / Auteur de la conférence Zuazua, Enrique.
[Virtualconference] A De Giorgi argument for $L^{\infty}$ solution to the Boltzmann equation without angular cutoff / Auteur de la conférence Yang, Tong.
[Virtualconference] An asymptotic preserving method for Levy Fokker Planck equation with fractional diffusion limit / Auteur de la conférence Wang, Li.
[Virtualconference] Bacterial movement by run and tumble: models, patterns, pathways, scales / Auteur de la conférence Perthame, Benoît.
[Virtualconference] Quantitative De Giorgi methods in kinetic theory / Auteur de la conférence Mouhot, Clément.
[Virtualconference] Stable and unstable steady states for the HMF model / Auteur de la conférence Mehats, Florian.
[Virtualconference] Highly-oscillatory evolution equations: averaging and numerics / Auteur de la conférence Lemou, Mohammed.
[Virtualconference] An inverse problem for a model of cell motion and chemotaxis / Auteur de la conférence Klingenberg, Christian.
[Virtualconference] Mean-field-type limits of interacting particle systems for multiple species / Auteur de la conférence Juengel, Ansgar.
[Virtualconference] Large stochastic systems of interacting particles / Auteur de la conférence Jabin, Pierre-Emmanuel.
[Virtualconference] Stabilization of random kinetic equations / Auteur de la conférence Herty, Michael.
[Virtualconference] Classical and quantum particles coupled to a vibrational environment / Auteur de la conférence Goudon, Thierry.
[Virtualconference] Partial regularity in time for the Landau equation with Coulomb interaction / Auteur de la conférence Golse, François.
[Virtualconference] Dynamical low-rank approximation for radiation transport / Auteur de la conférence Frank, Martin.
[Virtualconference] Large time asymptotics for evolution equations with mean field couplings / Auteur de la conférence Dolbeault, Jean.
[Virtualconference] Quasilinear approximation of Vlasov and Liouville equations / Auteur de la conférence Bardos, Claude.
[Virtualconference] Collective dynamics of quantized vortices in superfluidity and superconductivity / Auteur de la conférence Bao, Weizhu.
[Virtualconference] Modal based hypocoercivity methods on the torus and the real line with application to Goldstein-Taylor models / Auteur de la conférence Arnold, Anton.

Bibliographie

FILBET, Francis et MOUHOT, Clément. Analysis of spectral methods for the homogeneous Boltzmann equation. Transactions of the american mathematical society, 2011, vol. 363, no 4, p. 1947-1980. - http://dx.doi.org/10.1090/S0002-9947-2010-05303-6

HU, Jingwei, QI, Kunlun, et YANG, Tong. A New Stability and Convergence Proof of the Fourier--Galerkin Spectral Method for the Spatially Homogeneous Boltzmann Equation. SIAM Journal on Numerical Analysis, 2021, vol. 59, no 2, p. 613-633. - https://doi.org/10.1137/20M1351813

Hu.jpg

Sélection Signaler une erreur

TUTELLES

PARTENAIRES

Destination de la recherche

Raccourcis

Voir Aussi