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

TL;DR

This paper introduces a second order dynamical low-rank algorithm for 6D Vlasov--Poisson simulations, leveraging spectral methods and GPU acceleration to enable efficient, high-dimensional plasma physics computations on standard workstations.

Contribution

It develops a novel second order projector-splitting dynamical low-rank algorithm combined with spectral methods, enabling efficient 6D Vlasov simulations on modern hardware.

Findings

Simulations can be run on a single workstation.

GPU acceleration provides significant speedup.

The method accurately captures physical phenomena like filamentation.

Abstract

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 CFL condition free 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.