Vlasov on GPU (VOG Project)

TL;DR

This paper presents a GPU-accelerated semi-Lagrangian solver for Vlasov-Poisson equations, utilizing FFT-based reformulation and a { extdelta}f method to enable high-precision plasma simulations efficiently.

Contribution

It introduces a reformulated semi-Lagrangian approach compatible with GPU architectures and implements a { extdelta}f method for high-precision, efficient plasma simulations.

Findings

Successfully simulated Landau damping and KEEN waves.

Achieved high-precision results with GPU acceleration.

Demonstrated efficiency of FFT-based matrix operations.

Abstract

This work concerns the numerical simulation of the Vlasov-Poisson set of equations using semi- Lagrangian methods on Graphical Processing Units (GPU). To accomplish this goal, modifications to traditional methods had to be implemented. First and foremost, a reformulation of semi-Lagrangian methods is performed, which enables us to rewrite the governing equations as a circulant matrix operating on the vector of unknowns. This product calculation can be performed efficiently using FFT routines. Second, to overcome the limitation of single precision inherent in GPU, a {\delta}f type method is adopted which only needs refinement in specialized areas of phase space but not throughout. Thus, a GPU Vlasov-Poisson solver can indeed perform high precision simulations (since it uses very high order reconstruction methods and a large number of grid points in phase space). We show results for rather academic test cases on Landau damping and also for physically relevant phenomena such as the bump on tail instability and the simulation of Kinetic Electrostatic Electron Nonlinear (KEEN) waves.