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Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation

Published online by Cambridge University Press:  14 August 2013

Clément Mouhot ,
Lorenzo Pareschi  and
Thomas Rey
Clément Mouhot
Affiliation:
DPMMS, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.. [email protected]
Lorenzo Pareschi
Affiliation:
DMI, Università di Ferrara, Via Machiavelli 35, 44121 Ferrara, Italy.; [email protected]
Thomas Rey
Affiliation:
CSCAMM, University of Maryland, CSIC Building, Paint Branch Drive, College Park, MD 20740, USA.; [email protected]
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Abstract

Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically O(N2d + 1) where d is the dimension of the velocity space. In this paper, following the ideas introduced in [C. Mouhot and L. Pareschi, C. R. Acad. Sci. Paris Sér. I Math. 339 (2004) 71–76, C. Mouhot and L. Pareschi, Math. Comput. 75 (2006) 1833–1852], we derive fast summation techniques for the evaluation of discrete-velocity schemes which permits to reduce the computational cost from O(N2d + 1) to O(N̅dNd log2N), N̅ ≪ N, with almost no loss of accuracy.

Keywords

Boltzmann equationdiscrete-velocity approximationsdiscrete-velocity methodsfast summation methodsfarey seriesconvolutive decomposition
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 5 , September 2013 , pp. 1515 - 1531
Copyright
© EDP Sciences, SMAI, 2013

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