A Deterministic-stochastic Method for Computing the Boltzmann Collision Integral in O(MN) operations

Authors

Alexander Alekseenko, California State University, Northridge
Truong Nguyen, Wright State University
Aihua W. Wood, Air Force Institute of TechnologyFollow

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.

Comments

The "Link to Full Text" button on this page loads the cover page of the published full-text article, hosted at American Institute of Mathematical Sciences. The publisher, AIMS, retains permissions to re-use and distribute this article.

Reviewed at MR3810862

L_AT_EX-format title: A deterministic-stochastic method for computing the Boltzmann collision integral in $\mathcal{O}(MN)$ operations

DOI

10.3934/krm.2018047

Source Publication

Kinetic & Related Models

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