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.
Mots-clés : 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://www.numdam.org/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://www.numdam.org/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://www.numdam.org/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 , Volume 47 (2013) no. 5, pp. 1515-1531. doi : 10.1051/m2an/2013078. http://www.numdam.org/articles/10.1051/m2an/2013078/
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