A performance comparison of semi-Lagrangian discontinuous Galerkin and spline based Vlasov solvers in four dimensions

Highlights: • The SLDG method is efficient for high dimensional Vlasov simulation. • We obtain superior performance compared to a well established implementation. • The local nature of SLDG helps significantly in parallelization (e.g. on GPUs). • The performance in the asymptotic regime is a very poor predictor of accuracy. • First performance comparison of SLDG in more than two dimensions. -- Abstract: The purpose of the present paper is to compare two semi-Lagrangian methods in the context of the four-dimensional Vlasov–Poisson equation. More specifically, our goal is to compare the performance of the more recently developed semi-Lagrangian discontinuous Galerkin scheme to cubic spline interpolation, which is widely used in Eulerian Vlasov simulation. To that end, we perform simulations for nonlinear Landau damping and a two-stream instability and provide benchmarks for the SeLaLib and SLDG codes, both on a workstation and using MPI on a cluster. In addition, we will present results for the graphic processing unit (GPU) implementation contained in SLDG. We find that the semi-Lagrangian discontinuous Galerkin scheme shows a moderate improvement in run time for nonlinear Landau damping and a substantial improvement for the two-stream instability. It should be emphasized that these results are markedly different from results obtained in the asymptotic regime, which favor spline interpolation. Thus, we conclude that the traditional approach of evaluating numerical methods is misleading, even for short time simulations. In addition, the absence of any global communication in the semi-Lagrangian discontinuous Galerkin method gives it a decisive advantage for scaling to more than 256 cores.