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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 equation, discrete-velocity approximations, discrete-velocity methods, fast summation methods, farey series, convolutive decomposition
@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 },
pages = {1515--1531},
publisher = {EDP-Sciences},
volume = {47},
number = {5},
year = {2013},
doi = {10.1051/m2an/2013078},
mrnumber = {3100773},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013078/}
}
TY - JOUR AU - Mouhot, Clément AU - Pareschi, Lorenzo AU - Rey, Thomas TI - Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2013 SP - 1515 EP - 1531 VL - 47 IS - 5 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013078/ DO - 10.1051/m2an/2013078 LA - en ID - M2AN_2013__47_5_1515_0 ER -
%0 Journal Article %A Mouhot, Clément %A Pareschi, Lorenzo %A Rey, Thomas %T Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2013 %P 1515-1531 %V 47 %N 5 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013078/ %R 10.1051/m2an/2013078 %G en %F 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 , Tome 47 (2013) no. 5, pp. 1515-1531. doi: 10.1051/m2an/2013078
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