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- Title
A DETERMINISTIC-STOCHASTIC METHOD FOR COMPUTING THE BOLTZMANN COLLISION INTEGRAL IN O(MN) OPERATIONS.
- Authors
Alekseenko, Alexander; Nguyen, Truong; Wood, Aihua
- 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.
- Subjects
BOLTZMANN'S equation; COLLISION integrals; STOCHASTIC models; GALERKIN methods; DISCRETIZATION methods; SINGULAR value decomposition
- Publication
Kinetic & Related Models, 2018, Vol 11, Issue 5, p1211
- ISSN
1937-5093
- Publication type
Article
- DOI
10.3934/krm.2018047