A FAST SPECTRAL ALGORITHM FOR THE QUANTUM BOLTZMANN COLLISION OPERATOR
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Abstracthis 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.
CitationHu, J., & Ying, L. (2012). A fast spectral algorithm for the quantum Boltzmann collision operator. Communications in Mathematical Sciences, 10(3), 989–999. doi:10.4310/cms.2012.v10.n3.a13
SponsorsJ.H. would like to thank KAUST for their generous support. L.Y. was supported in part by the NSF under CAREER grant DMS-0846501.