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

Abstract

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 [27,28], 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.

v2: 22 pages, improvement of the presentation and more details given in some proofs. arXiv admin note: text overlap with arXiv:1106.1020 by other authors

References in corpus (2)

• A Numerical Scheme for the Quantum Boltzmann Equation Efficient in the Fluid Regime
• Fast conservative and entropic numerical methods for the Boson Boltzmann equation

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