Fast algorithms for computing the Boltzmann collision operator

Cl\'ement Mouhot (CEREMADE); Lorenzo Pareschi (DPT OF MATH.; Univ. of Ferrara)

Fast algorithms for computing the Boltzmann collision operator

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arxiv math/0607542 v1 pith:LIDLKGXA submitted 2006-07-21 math.AP cs.NAmath.NA

Fast algorithms for computing the Boltzmann collision operator

Cl\'ement Mouhot (CEREMADE) , Lorenzo Pareschi (DPT of Math. , Univ. of Ferrara) This is my paper

classification math.AP cs.NAmath.NA

keywords algorithmscollisionfastboltzmanncomputingoperatorschemesspectral

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The development of accurate and fast numerical schemes for the five fold Boltzmann collision integral represents a challenging problem in scientific computing. For a particular class of interactions, including the so-called hard spheres model in dimension three, we are able to derive spectral methods that can be evaluated through fast algorithms. These algorithms are based on a suitable representation and approximation of the collision operator. Explicit expressions for the errors in the schemes are given and spectral accuracy is proved. Parallelization properties and adaptivity of the algorithms are also discussed.

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Cited by 1 Pith paper

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On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law
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Power-law distributions arise in colliding hard-sphere systems from Maxwell-Boltzmann when starting far from equilibrium, with scale-free intermediate dynamics and open scale-free boundaries.