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

Clément Mouhot; Lorenzo Pareschi; Thomas Rey

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 5, page 1515-1531
  • ISSN: 0764-583X

Abstract

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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(N2d + 1) where d is the dimension of the velocity space. In this paper, following the ideas introduced in [C. Mouhot and L. Pareschi, C. R. Acad. Sci. Paris Sér. I Math. 339 (2004) 71–76, C. Mouhot and L. Pareschi, Math. Comput. 75 (2006) 1833–1852], 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(N̅dNd log2N), N̅ ≪ N, with almost no loss of accuracy.

How to cite

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Mouhot, Clément, Pareschi, Lorenzo, and Rey, Thomas. "Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.5 (2013): 1515-1531. <http://eudml.org/doc/273302>.

@article{Mouhot2013,
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(N2d + 1) where d is the dimension of the velocity space. In this paper, following the ideas introduced in [C. Mouhot and L. Pareschi, C. R. Acad. Sci. Paris Sér. I Math. 339 (2004) 71–76, C. Mouhot and L. Pareschi, Math. Comput. 75 (2006) 1833–1852], 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(N̅dNd log2N), N̅ ≪ N, with almost no loss of accuracy.},
author = {Mouhot, Clément, Pareschi, Lorenzo, Rey, Thomas},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Boltzmann equation; discrete-velocity approximations; discrete-velocity methods; fast summation methods; farey series; convolutive decomposition; Farey series},
language = {eng},
number = {5},
pages = {1515-1531},
publisher = {EDP-Sciences},
title = {Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation},
url = {http://eudml.org/doc/273302},
volume = {47},
year = {2013},
}

TY - JOUR
AU - Mouhot, Clément
AU - Pareschi, Lorenzo
AU - Rey, Thomas
TI - Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 5
SP - 1515
EP - 1531
AB - 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(N2d + 1) where d is the dimension of the velocity space. In this paper, following the ideas introduced in [C. Mouhot and L. Pareschi, C. R. Acad. Sci. Paris Sér. I Math. 339 (2004) 71–76, C. Mouhot and L. Pareschi, Math. Comput. 75 (2006) 1833–1852], 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(N̅dNd log2N), N̅ ≪ N, with almost no loss of accuracy.
LA - eng
KW - Boltzmann equation; discrete-velocity approximations; discrete-velocity methods; fast summation methods; farey series; convolutive decomposition; Farey series
UR - http://eudml.org/doc/273302
ER -

References

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