Communications in Mathematical Sciences

Volume 10 (2012)

Number 3

A fast spectral algorithm for the quantum Boltzmann collision operator

Pages: 989 – 999

(Fast Communication)

DOI: http://dx.doi.org/10.4310/CMS.2012.v10.n3.a13

Authors

Jingwei Hu (Institute for Computational Engineering and Sciences, The University of Texas at Austin)

Lexing Ying (Institute for Computational Engineering and Sciences, The University of Texas at Austin)

Abstract

This paper introduces a fast spectral algorithm for the quantum Boltzmann collision operator. In the usual spectral framework, one of the terms in the operator cannot be evaluated efficiently. The new approach is based on the fundamental property of the exponential function which allows one to construct a new decomposition of the collision kernel to speed up the computation. Numerical results in 2-D and 3-D for both the Bose gas and the Fermi gas are presented to illustrate the accuracy and efficiency of the method.

Keywords

quantum Boltzmann equation, fast spectral method

2010 Mathematics Subject Classification

35Q20, 65M70

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