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

Clément Mouhot; Lorenzo Pareschi; Thomas Rey

doi:10.1051/m2an/2013078

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

Clément Mouhot
, Lorenzo Pareschi
, Thomas Rey

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

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 [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(N^2d+1) to O(N^dN^d log₂ N), N ≪ N, with almost no loss of accuracy.

Original language	English
Pages (from-to)	1515-1531
Number of pages	17
Journal	Mathematical Modelling and Numerical Analysis
Volume	47
Issue number	5
DOIs	https://doi.org/10.1051/m2an/2013078
Publication status	Published - Sept 2013

Keywords

Boltzmann equation
Convolutive decomposition
Discrete-velocity approximations
Discrete-velocity methods
Farey series
Fast summation methods

ASJC Scopus subject areas

Analysis
Numerical Analysis
Modelling and Simulation
Computational Mathematics
Applied Mathematics

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10.1051/m2an/2013078

Cite this

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title = "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(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 S{\'e}r. 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(NdNd log2 N), N ≪ N, with almost no loss of accuracy.",

keywords = "Boltzmann equation, Convolutive decomposition, Discrete-velocity approximations, Discrete-velocity methods, Farey series, Fast summation methods",

author = "Cl{\'e}ment Mouhot and Lorenzo Pareschi and Thomas Rey",

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doi = "10.1051/m2an/2013078",

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TY - JOUR

T1 - Convolutive decomposition and fast summation methods for discrete-velocity approximations of the boltzmann equation

AU - Mouhot, Clément

AU - Pareschi, Lorenzo

AU - Rey, Thomas

PY - 2013/9

Y1 - 2013/9

N2 - 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(NdNd log2 N), N ≪ N, with almost no loss of accuracy.

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(NdNd log2 N), N ≪ N, with almost no loss of accuracy.

KW - Boltzmann equation

KW - Convolutive decomposition

KW - Discrete-velocity approximations

KW - Discrete-velocity methods

KW - Farey series

KW - Fast summation methods

UR - https://www.scopus.com/pages/publications/84996142338

U2 - 10.1051/m2an/2013078

DO - 10.1051/m2an/2013078

M3 - Article

AN - SCOPUS:84996142338

SN - 0764-583X

VL - 47

SP - 1515

EP - 1531

JO - Mathematical Modelling and Numerical Analysis

JF - Mathematical Modelling and Numerical Analysis

IS - 5

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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