Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation

Details Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation

2012-01-19

arxiv.org/abs/1201.3986v1

Mathematics

Numerical Analysis

20 pages

Scientific paper

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 [26,27], 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 $O(\bar{N}^d N^d\log_2 N)$, $\bar{N} << N$, with almost no loss of accuracy.

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