Fast Algorithms for Discrete Velocity Models of Boltzmann Equation

I added a link to a paper I wrote with C. Mouhot and L. Pareschi: Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation. It deals with a class of algorithms for computing the Boltzmann collision operator for hard spheres, and therefore computing the solutions to the Boltzmann equation. This class of algorithms is known as discrete-velocity methods (DVM), and is highly stable, due to the nice positivity and conservation properties of the schemes. 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, 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(Nd log N), with almost no loss of accuracy.