Dans cette Note nous présentons des méthodes pour le développement de schémas numériques rapides pour l'intégrale de collision de Boltzmann. Ces schémas sont basés sur la combinaison d'une représentation proche de celle de Carleman et d'une approximation angulaire appropriée. Pour le modèle des sphères dures en dimension trois, nous en déduisons des méthodes spectrales qui peuvent être évaluées par des algorithmes rapides. Nous donnons également des estimations d'erreur et un résultat de précision spectrale.
In this Note we present methods for the development of fast numerical schemes for the Boltzmann collision integral. These schemes are based on a combination of a Carleman-like representation together with a suitable angular approximation. For the hard spheres model in dimension three, we are able to derive spectral methods that can be evaluated through fast algorithms. Estimates for the errors and spectral accuracy are also given.
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@article{CRMATH_2004__339_1_71_0, author = {Mouhot, Cl\'ement and Pareschi, Lorenzo}, title = {Fast methods for the {Boltzmann} collision integral}, journal = {Comptes Rendus. Math\'ematique}, pages = {71--76}, publisher = {Elsevier}, volume = {339}, number = {1}, year = {2004}, doi = {10.1016/j.crma.2004.04.010}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2004.04.010/} }
TY - JOUR AU - Mouhot, Clément AU - Pareschi, Lorenzo TI - Fast methods for the Boltzmann collision integral JO - Comptes Rendus. Mathématique PY - 2004 SP - 71 EP - 76 VL - 339 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2004.04.010/ DO - 10.1016/j.crma.2004.04.010 LA - en ID - CRMATH_2004__339_1_71_0 ER -
%0 Journal Article %A Mouhot, Clément %A Pareschi, Lorenzo %T Fast methods for the Boltzmann collision integral %J Comptes Rendus. Mathématique %D 2004 %P 71-76 %V 339 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2004.04.010/ %R 10.1016/j.crma.2004.04.010 %G en %F CRMATH_2004__339_1_71_0
Mouhot, Clément; Pareschi, Lorenzo. Fast methods for the Boltzmann collision integral. Comptes Rendus. Mathématique, Tome 339 (2004) no. 1, pp. 71-76. doi : 10.1016/j.crma.2004.04.010. http://archive.numdam.org/articles/10.1016/j.crma.2004.04.010/
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☆ Support by the European network HYKE, funded by the EC as contract HPRN-CT-2002-00282, is acknowledged.