Geodesic
Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 5, pp. 1515-1531

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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.

DOI : 10.1051/m2an/2013078
Classification : 65T50, 68Q25, 74S25, 76P05
Keywords: Boltzmann equation, discrete-velocity approximations, discrete-velocity methods, fast summation methods, farey series, convolutive decomposition 
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     author = {Mouhot, Cl\'ement and Pareschi, Lorenzo and Rey, Thomas},
     title = {Convolutive decomposition and fast summation methods for discrete-velocity approximations of the {Boltzmann} equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1515--1531},
     publisher = {EDP-Sciences},
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     mrnumber = {3100773},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013078/}
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Mouhot, Clément; Pareschi, Lorenzo; Rey, Thomas. Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 5, pp. 1515-1531. doi: 10.1051/m2an/2013078

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