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

External document link

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

Date

2006

Journal name

Mathematics of Computation

Volume

Number

256

Pages

1833-1852

Metadata

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Author(s)

Pareschi, Lorenzo
Mouhot, Clément

Abstract (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.

Subjects / Keywords

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