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.
@article{M2AN_2013__47_5_1515_0,
author = {Mouhot, Cl\'ement and Pareschi, Lorenzo and Rey, Thomas},
title = {Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {47},
year = {2013},
pages = {1515-1531},
doi = {10.1051/m2an/2013078},
mrnumber = {3100773},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2013__47_5_1515_0}
}
Mouhot, Clément; Pareschi, Lorenzo; Rey, Thomas. Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 47 (2013) pp. 1515-1531. doi : 10.1051/m2an/2013078. http://gdmltest.u-ga.fr/item/M2AN_2013__47_5_1515_0/
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