Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2013

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

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 [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.

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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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Clément Mouhot, Lorenzo Pareschi, Thomas Rey. Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation. ESAIM: Mathematical Modelling and Numerical Analysis, 2013, 47 (5), pp.1515-1531. ⟨10.1051/m2an/2013078⟩. ⟨hal-00661151v2⟩
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