[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.
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@article{CRMATH_2003__337_5_353_0,
author = {Antoine, Xavier and Lemou, M.},
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},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(03)00345-5/}
}
TY - JOUR AU - Antoine, Xavier AU - Lemou, M. TI - Wavelet approximations of a collision operator in kinetic theory JO - Comptes Rendus. Mathématique PY - 2003 SP - 353 EP - 358 VL - 337 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(03)00345-5/ DO - 10.1016/S1631-073X(03)00345-5 LA - en ID - CRMATH_2003__337_5_353_0 ER -
%0 Journal Article %A Antoine, Xavier %A Lemou, M. %T Wavelet approximations of a collision operator in kinetic theory %J Comptes Rendus. Mathématique %D 2003 %P 353-358 %V 337 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(03)00345-5/ %R 10.1016/S1631-073X(03)00345-5 %G en %F CRMATH_2003__337_5_353_0
Antoine, Xavier; Lemou, M. Wavelet approximations of a collision operator in kinetic theory. Comptes Rendus. Mathématique, Tome 337 (2003) no. 5, pp. 353-358. doi : 10.1016/S1631-073X(03)00345-5. http://www.numdam.org/articles/10.1016/S1631-073X(03)00345-5/
[1] Adaptive solution of partial differential equations in multiwavelet bases, J. Comput. Phys., Volume 182 (2002) no. 1, pp. 149-190
[2] X. Antoine, M. Lemou, Multiwavelet approximations of collisional operators in kinetic theory, in preparation
[3] Fast wavelet transforms and numerical algorithms. I, Comm. Pure Appl. Math., Volume 44 (1991) no. 2, pp. 141-183
[4] Fast algorithms for numerical, conservative and entropy approximations of the Fokker–Planck–Landau equation, J. Comput. Phys., Volume 133 (1997), pp. 310-322
[5] An entropy scheme for the Fokker–Planck collision of plasma kinetic theory, Numer. Math., Volume 68 (1994), pp. 239-262
[6] Fast spectral methods for the Fokker–Planck–Landau collision operator, J. Comput. Phys., Volume 165 (2000) no. 1, pp. 216-236
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☆ This work was supported by an “ATIP-Jeunes Chercheurs” CNRS project.
