[Approximations par ondelettes d'un opérateur de collision en théorie cinétique]
Cette Note présente un schéma conservatif et entropique basé sur l'utilisation des ondelettes pour l'équation de Fokker–Planck–Landau isotrope qui modélise l'évolution des particules chargées dans un plasma. La présente approche possède à la fois les propriétés des schémas aux différences finies (conservation et entropie) et celles des méthodes spectrales (essentiellement la précision) qui sont développés dans la littérature. De plus, l'approche ondelette fournit un algorithme rapide d'évaluation de l'opérateur de collision. Ce travail constitue un premier pas vers le développement d'approximations par ondelettes d'opérateurs de collision plus complexes.
This Note is devoted to the derivation of conservative and entropic fast wavelet approximations for the isotropic Fokker–Planck–Landau collision operator arising in the modeling of charged particles in plasma physics. The present approach combines the advantages of both the finite difference schemes (conservation and entropy) and the spectral methods (accuracy) which are developed in the literature. Furthermore, the wavelet approach provides a fast algorithm for the evaluation of such a collision operator. The present work is a first step to the development of wavelet approximations to more complex collision operators in kinetic theory.
Accepté le :
Publié le :
Xavier Antoine 1 ; M. Lemou 1
@article{CRMATH_2003__337_5_353_0,
author = {Xavier Antoine and M. Lemou},
title = {Wavelet approximations of a collision operator in kinetic theory},
journal = {Comptes Rendus. Math\'ematique},
pages = {353--358},
publisher = {Elsevier},
volume = {337},
number = {5},
year = {2003},
doi = {10.1016/S1631-073X(03)00345-5},
language = {en},
}
Xavier Antoine; M. Lemou. Wavelet approximations of a collision operator in kinetic theory. Comptes Rendus. Mathématique, Volume 337 (2003) no. 5, pp. 353-358. doi : 10.1016/S1631-073X(03)00345-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00345-5/
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- Numerical methods for kinetic equations, Acta Numerica, Volume 23 (2014), p. 369 | DOI:10.1017/s0962492914000063
- Binary Interaction Algorithms for the Simulation of Flocking and Swarming Dynamics, Multiscale Modeling Simulation, Volume 11 (2013) no. 1, p. 1 | DOI:10.1137/120868748
- A finite element/Fourier treatment of the Fokker–Planck equation, Journal of Computational Physics, Volume 231 (2012) no. 18, p. 6192 | DOI:10.1016/j.jcp.2012.06.004
- Implicit Schemes for the Fokker–Planck–Landau Equation, SIAM Journal on Scientific Computing, Volume 27 (2005) no. 3, p. 809 | DOI:10.1137/040609422
Cité par 5 documents. Sources : Crossref
☆ This work was supported by an “ATIP-Jeunes Chercheurs” CNRS project.
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