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Mathematics of Computation

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Fast algorithms for computing the Boltzmann collision operator

Authors: Clément Mouhot and Lorenzo Pareschi
Journal: Math. Comp. 75 (2006), 1833-1852
MSC (2000): Primary 65T50, 68Q25, 74S25, 76P05
Published electronically: July 12, 2006
MathSciNet review: 2240637
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Abstract: 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.

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Additional Information

Clément Mouhot
Affiliation: UMPA, ENS Lyon, 46 allée d’Italie, 69364 Lyon Cedex 07, France

Lorenzo Pareschi
Affiliation: Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, 44100 Ferrara, Italy

Keywords: Boltzmann equation, spectral methods, fast Fourier transform, fast algorithms
Received by editor(s): February 7, 2004
Received by editor(s) in revised form: March 13, 2005
Published electronically: July 12, 2006
Additional Notes: The first author was supported by the European network HYKE, funded by the EC as contract HPRN-CT-2002-00282
Article copyright: © Copyright 2006 by the authors