A fast algorithm for the energy space boson Boltzmann collision operator
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- by Jingwei Hu and Lexing Ying PDF
- Math. Comp. 84 (2015), 271-288 Request permission
Abstract:
This paper introduces a fast algorithm for the energy space boson Boltzmann collision operator. Compared to the direct $O(N^3)$ calculation and the previous $O(N^2\log N)$ method [Markowich and Pareschi, 2005], the new algorithm runs in complexity $O(N\log ^2N)$, which is optimal up to a logarithmic factor ($N$ is the number of grid points in energy space). The basic idea is to partition the 3-D summation domain recursively into elementary shapes so that the summation within each shape becomes a special double convolution that can be computed efficiently by the fast Fourier transform. Numerical examples are presented to illustrate the efficiency and accuracy of the proposed algorithm.References
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Additional Information
- Jingwei Hu
- Affiliation: Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, 1 University Station, C0200, Austin, Texas 78712
- Email: hu@ices.utexas.edu
- Lexing Ying
- Affiliation: Department of Mathematics and Institute for Computational and Mathematical Engineering (ICME), Stanford University, 450 Serra Mall, Bldg 380, Stanford, California 94305
- Email: lexing@math.stanford.edu
- Received by editor(s): June 2, 2012
- Received by editor(s) in revised form: December 12, 2012, and December 27, 2012
- Published electronically: March 21, 2014
- Additional Notes: The first author was supported by an ICES Postdoctoral Fellowship
The second author was partially supported by NSF under CAREER award DMS-0846501 - © Copyright 2014 American Mathematical Society
- Journal: Math. Comp. 84 (2015), 271-288
- MSC (2010): Primary 35Q20, 82C10, 65D32, 44A35, 65T50
- DOI: https://doi.org/10.1090/S0025-5718-2014-02824-X
- MathSciNet review: 3266960