Fast algorithms for computing the Boltzmann collision operator

Pareschi, Lorenzo; Mouhot, Clément

Pareschi, Lorenzo; Mouhot, Clément (2006), Fast algorithms for computing the Boltzmann collision operator, Mathematics of Computation, 75, 256, p. 1833-1852

Type

Article accepté pour publication ou publié

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http://hal.archives-ouvertes.fr/hal-00087285/en/

Date

2006

Nom de la revue

Mathematics of Computation

Volume

Numéro

256

Pages

1833-1852

Métadonnées

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Auteur(s)

Pareschi, Lorenzo
Mouhot, Clément

Résumé (EN)

The development of accurate and fast numerical schemes for the five fold Boltzmann collision integral represents a challenging problem in scientific computing. For a particular class of interactions, including the so-called hard spheres model in dimension three, we are able to derive spectral methods that can be evaluated through fast algorithms. These algorithms are based on a suitable representation and approximation of the collision operator. Explicit expressions for the errors in the schemes are given and spectral accuracy is proved. Parallelization properties and adaptivity of the algorithms are also discussed.

Mots-clés

fast algorithms; discrete velocity methods; spectral methods; Boltzmann equation