A semi-Lagrangian discontinuous Galerkin method for drift-kinetic simulations on GPUs

Abstract: In this paper, we demonstrate the efficiency of using semi-Lagrangian discontinuous Galerkin methods to solve the drift-kinetic equation using graphic processing units (GPUs). In this setting we propose a second order splitting scheme and a 2d semi-Lagrangian scheme in the poloidal plane. The resulting method is able to conserve mass up to machine precision, allows us to take large time steps due to the absence of a CFL condition and provides local data dependency which is essential to obtain good performance on state-of-the art high-performance computing systems. We report simulations of a drift-kinetic ion temperature gradient (ITG) instability and show that our implementation achieves a performance of up to 600 GB/s on an A100 GPU.