A Deterministic-stochastic Method for Computing the Boltzmann Collision Integral in O(MN) operations
Document Type
Article
Publication Date
10-2018
Abstract
We developed and implemented a numerical algorithm for evaluating the Boltzmann collision integral with O(MN) operations, where N is the number of the discrete velocity points and M < N. At the base of the algorithm are nodal-discontinuous Galerkin discretizations of the collision operator on uniform grids and a bilinear convolution form of the Galerkin projection of the collision operator. Efficiency of the algorithm is achieved by applying singular value decomposition compression of the discrete collision kernel and by approximating the kinetic solution by a sum of Maxwellian streams using a stochastic likelihood maximization algorithm. Accuracy of the method is established on solutions to the problem of spatially homogeneous relaxation.
Source Publication
Kinetic & Related Models (ISSN 1937-5077)
Recommended Citation
Alekseenko, A., Nguyen, T., & Wood, A. W. (2018). A deterministic-stochastic method for computing the Boltzmann collision integral in $\mathcal{O}(MN)$ operations. Kinetic & Related Models, 11(5), 1211–1234. https://doi.org/10.3934/krm.2018047
Comments
This article is published by American Institute of Mathematical Sciences (AIMS), licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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Reviewed at MR3810862
LATEX-format title: A deterministic-stochastic method for computing the Boltzmann collision integral in $\mathcal{O}(MN)$ operations