Mathematical Problems in Mechanics
Fast methods for the Boltzmann collision integral
Comptes Rendus. Mathématique, Volume 339 (2004) no. 1, pp. 71-76.

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.

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.

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DOI: 10.1016/j.crma.2004.04.010
Mouhot, Clément 1; Pareschi, Lorenzo 2

1 École normale supérieure de Lyon, UMPA, 46, allée d'Italie, 69364 Lyon cedex 07, France
2 Department of Mathematics, University of Ferrara, via Machiavelli 35, 35100 Ferrara, Italy
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Mouhot, Clément; Pareschi, Lorenzo. Fast methods for the Boltzmann collision integral. Comptes Rendus. Mathématique, Volume 339 (2004) no. 1, pp. 71-76. doi : 10.1016/j.crma.2004.04.010. http://www.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.