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 features such as filamentation and Landau damping. In this paper, we introduce the Ensign software framework, which facilitates the efficient implementation of dynamical low-rank algorithms on modern multi-core CPU as well as GPU based systems. In particular, we illustrate its features with the help of a first-order projector-splitting integrator. Then, we propose a new second-order projector-splitting based dynamical low-rank algorithm for the full six-dimensional Vlasov--Poisson equations and implement it using our software framework. An exponential integrator based Fourier spectral method is employed to obtain a numerical method that is unconditionally stable but fully explicit. The presented numerical results demonstrate that 6D simulations can be run on a single workstation, as well as highlight the significant speedup that can be obtained using GPUs.