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Pré-Publication, Document De Travail Année : 2012

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

Lorenzo Pareschi
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Thomas Rey

Résumé

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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Dates et versions

hal-00661151 , version 1 (18-01-2012)
hal-00661151 , version 2 (13-12-2012)

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Citer

Clément Mouhot, Lorenzo Pareschi, Thomas Rey. Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation. 2012. ⟨hal-00661151v1⟩

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