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

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

doi:10.1016/j.jcp.2024.113053

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

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

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	113053
Journal	Journal of Computational Physics
Volume	510
DOIs	https://doi.org/10.1016/j.jcp.2024.113053
State	Published - Aug 1 2024

Funding

This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).This material is based upon work partially supported by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, as part of their Applied Mathematics Research Program; the U.S. Department of Energy Office of Science, Office of Fusion Energy Science as part of their Fusion Research Energy Program; and the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory (ORNL), managed by UT-Battelle, LLC for the U.S. Department of Energy under Contract No. De-AC05-00OR22725. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.Stefan Schnake, Coleman Kendrick, Eirik Endeve, Miroslav Stoyanov, Steven Hahn, Cory D. Hauck, David L. Green, Phil Snyder, and John Canik report financial support was provided by US Department of Energy. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Keywords

Discontinuous Galerkin
Implicit-explicit
Kinetic equation
Lenard–Bernstein
Sparse grids
Vlasov–Poisson

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10.1016/j.jcp.2024.113053

Cite this

@article{3192f904cb9a4925837ae3cfecf952b4,

title = "Sparse-grid discontinuous Galerkin methods for the Vlasov–Poisson–Lenard–Bernstein model",

abstract = "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.",

keywords = "Discontinuous Galerkin, Implicit-explicit, Kinetic equation, Lenard–Bernstein, Sparse grids, Vlasov–Poisson",

author = "Stefan Schnake and Coleman Kendrick and Eirik Endeve and Miroslav Stoyanov and Steven Hahn and Hauck, \{Cory D.\} and Green, \{David L.\} and Phil Snyder and John Canik",

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year = "2024",

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doi = "10.1016/j.jcp.2024.113053",

language = "English",

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T1 - Sparse-grid discontinuous Galerkin methods for the Vlasov–Poisson–Lenard–Bernstein model

AU - Schnake, Stefan

AU - Kendrick, Coleman

AU - Endeve, Eirik

AU - Stoyanov, Miroslav

AU - Hahn, Steven

AU - Hauck, Cory D.

AU - Green, David L.

AU - Snyder, Phil

AU - Canik, John

PY - 2024/8/1

Y1 - 2024/8/1

N2 - 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.

AB - 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.

KW - Discontinuous Galerkin

KW - Implicit-explicit

KW - Kinetic equation

KW - Lenard–Bernstein

KW - Sparse grids

KW - Vlasov–Poisson

UR - https://www.scopus.com/pages/publications/85193434157

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DO - 10.1016/j.jcp.2024.113053

M3 - Article

AN - SCOPUS:85193434157

SN - 0021-9991

VL - 510

JO - Journal of Computational Physics

JF - Journal of Computational Physics

M1 - 113053

ER -

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

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Keywords

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