Fast algorithms for computing the Boltzmann collision operator

Abstract

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.

22 pages

References in corpus (2)

• Regularity theory for the spatially homogeneous Boltzmann equation with cut-off
• Quantitative lower bounds for the full Boltzmann equation, Part I: Periodic boundary conditions

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