*Clément Mouhot, Lorenzo Pareschi, Thomas Rey*

(19/01/2012 arXiv:1201:3986,

*Math. Mod. Num. Anal.*47, 2013, 1515-1531)

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(

*N*^{2d+1}) where*d*is the dimension of the velocity space.
In this paper, following the ideas introduced in

*C.Mouhot, L.Pareschi, Math. Comp.75, 2006*, we derive fast summation techniques for the evaluation of discrete-velocity schemes which permits to reduce the computational cost from O(*N*^{2d+1}) to O(*N*^{d}log*N*) with almost no loss of accuracy.**Links**