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

Schnake, Stefan; Kendrick, Coleman; Endeve, Eirik; Stoyanov, Miroslav; Hahn, Steven; Hauck, Cory D.; Green, David L.; Snyder, Phil; Canik, John

doi:10.1016/j.jcp.2024.113053

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

Journal Article · 07 May 2024 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2024.113053 · OSTI ID:2394732

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Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
Commonwealth Scientific and Industrial Research Organisation (CSIRO), Mayfield West, NSW (Australia)
Type One Energy Group, Oak Ridge, TN (United States)

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. Here 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.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Fusion Energy Sciences (FES); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 2394732

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 510; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
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Title: Sparse-grid discontinuous Galerkin methods for the Vlasov–Poisson–Lenard–Bernstein model

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