Efficient 6D Vlasov simulation using the dynamical low-rank framework Ensign

Running kinetic simulations using grid-based methods is extremely expensive due to the up to six-dimensional phase space. Recently, it has been shown that dynamical low-rank algorithms can drastically reduce the required computational effort, while still accurately resolving important physical featu...

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Bibliographic Details
Published in:Computer physics communications Vol. 280; p. 108489
Main Authors: Cassini, Fabio, Einkemmer, Lukas
Format: Journal Article
Language:English
Published: Elsevier B.V 01.11.2022
Subjects:
Dynamical low-rank approximation
Exponential integrators
General Purpose computing on Graphic Processing Unit (GPGPU)
High-dimensional PDEs
Projector-splitting integrator
Vlasov–Poisson equations
Dynamical low-rank approximation
Projector-splitting integrator
General Purpose computing on Graphic Processing Unit (GPGPU)
Exponential integrators
High-dimensional PDEs
Vlasov–Poisson equations
ISSN:0010-4655
Online Access:Get full text
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Summary:Running kinetic simulations using grid-based methods is extremely expensive due to the up to six-dimensional phase space. Recently, it has been shown that dynamical low-rank algorithms can drastically reduce the required computational effort, while still accurately resolving important physical features such as filamentation and Landau damping. In this paper, we propose a new second order projector-splitting dynamical low-rank algorithm for the full six-dimensional Vlasov–Poisson equations. An exponential integrator based Fourier spectral method is employed to obtain a numerical scheme that is free of a CFL condition but still fully explicit. The resulting method is implemented with the aid of Ensign, a software framework which facilitates the efficient implementation of dynamical low-rank algorithms on modern multi-core CPU as well as GPU based systems. Its usage and features are briefly described in the paper as well. The presented numerical results demonstrate that 6D simulations can be run on a single workstation and highlight the significant speedup that can be obtained using GPUs.
ISSN:0010-4655
DOI:10.1016/j.cpc.2022.108489