The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov-Maxwell equations

Oleksandr Koshkarov; Gianmarco Manzini; Gian Luca Delzanno; Cecilia Pagliantini; Vadim Roytershteyn

doi:10.1016/j.cpc.2021.107866

The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov-Maxwell equations

Oleksandr Koshkarov (Corresponding author), Gianmarco Manzini, Gian Luca Delzanno (Corresponding author), Cecilia Pagliantini, Vadim Roytershteyn

Center for Analysis, Scientific Computing and Applications

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

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Abstract

We discuss the development, analysis, implementation, and numerical assessment of a spectral method for the numerical simulation of the three-dimensional Vlasov-Maxwell equations. The method is based on a spectral expansion of the velocity space with the asymmetrically weighted Hermite functions. The resulting system of time-dependent nonlinear equations is discretized by the discontinuous Galerkin (DG) method in space and by the method of lines for the time integration using explicit Runge-Kutta integrators. The resulting code, called Spectral Plasma Solver (SPS-DG), is successfully applied to standard plasma physics benchmarks to demonstrate its accuracy, robustness, and parallel scalability.

Original language	English
Article number	107866
Number of pages	35
Journal	Computer Physics Communications
Volume	264
DOIs	https://doi.org/10.1016/j.cpc.2021.107866
Publication status	Published - Jul 2021

Keywords

3-D Vlasov–Maxwell equations
AW Hermite discretization
Discontinuous Galerkin method

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10.1016/j.cpc.2021.107866

arXiv 2004.12010v1Final author version , 3.5 MB

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title = "The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov-Maxwell equations",

abstract = " We discuss the development, analysis, implementation, and numerical assessment of a spectral method for the numerical simulation of the three-dimensional Vlasov-Maxwell equations. The method is based on a spectral expansion of the velocity space with the asymmetrically weighted Hermite functions. The resulting system of time-dependent nonlinear equations is discretized by the discontinuous Galerkin (DG) method in space and by the method of lines for the time integration using explicit Runge-Kutta integrators. The resulting code, called Spectral Plasma Solver (SPS-DG), is successfully applied to standard plasma physics benchmarks to demonstrate its accuracy, robustness, and parallel scalability. ",

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T1 - The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov-Maxwell equations

AU - Koshkarov, Oleksandr

AU - Manzini, Gianmarco

AU - Delzanno, Gian Luca

AU - Pagliantini, Cecilia

AU - Roytershteyn, Vadim

PY - 2021/7

Y1 - 2021/7

N2 - We discuss the development, analysis, implementation, and numerical assessment of a spectral method for the numerical simulation of the three-dimensional Vlasov-Maxwell equations. The method is based on a spectral expansion of the velocity space with the asymmetrically weighted Hermite functions. The resulting system of time-dependent nonlinear equations is discretized by the discontinuous Galerkin (DG) method in space and by the method of lines for the time integration using explicit Runge-Kutta integrators. The resulting code, called Spectral Plasma Solver (SPS-DG), is successfully applied to standard plasma physics benchmarks to demonstrate its accuracy, robustness, and parallel scalability.

AB - We discuss the development, analysis, implementation, and numerical assessment of a spectral method for the numerical simulation of the three-dimensional Vlasov-Maxwell equations. The method is based on a spectral expansion of the velocity space with the asymmetrically weighted Hermite functions. The resulting system of time-dependent nonlinear equations is discretized by the discontinuous Galerkin (DG) method in space and by the method of lines for the time integration using explicit Runge-Kutta integrators. The resulting code, called Spectral Plasma Solver (SPS-DG), is successfully applied to standard plasma physics benchmarks to demonstrate its accuracy, robustness, and parallel scalability.

KW - physics.comp-ph

KW - physics.plasm-ph

KW - physics.space-ph

KW - 3-D Vlasov–Maxwell equations

KW - AW Hermite discretization

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DO - 10.1016/j.cpc.2021.107866

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VL - 264

JO - Computer Physics Communications

JF - Computer Physics Communications

M1 - 107866

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The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov-Maxwell equations

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