Sparse-grid discontinuous Galerkin methods for the Vlasov–Poisson–Lenard–Bernstein model

Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov–Poisson–Lenard–Bernstein (VPLB) model. This model has applications to plasma physics...

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Bibliographic Details
Published in:Journal of computational physics 2024-08, Vol.510, p.113053, Article 113053
Main Authors: Schnake, Stefan, Kendrick, Coleman, Endeve, Eirik, Stoyanov, Miroslav, Hahn, Steven, Hauck, Cory D., Green, David L., Snyder, Phil, Canik, John
Format: Article
Language:English
Subjects:
Discontinuous Galerkin
Implicit-explicit
Kinetic equation
Lenard-Bernstein
MATHEMATICS AND COMPUTING
Sparse grids
Vlasov-Poisson
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Summary:Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov–Poisson–Lenard–Bernstein (VPLB) model. This model has applications to plasma physics and is simulated in two reduced geometries: a 0x3v space homogeneous geometry and a 1x3v slab geometry. We use the discontinuous Galerkin (DG) method as a base discretization due to its high-order accuracy and ability to preserve important structural properties of partial differential equations. We utilize a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria. We analyze the proposed sparse-grid methods on a suite of three test problems by computing the savings afforded by sparse-grids in comparison to standard solutions of the DG method. The results are obtained using the adaptive sparse-grid discretization library ASGarD.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2024.113053