  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 with the de facto
standard in Eulerian Vlasov simulation (i.e. using cubic spline interpolation).
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).
  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 All-to-All communication in the
semi-Lagrangian discontinuous Galerkin method gives it a decisive advantage for
scaling to more than 256 cores.
