Solving the Vlasov equation for one-dimensional models with long range interactions on a GPU

We present a GPU parallel implementation of the numeric integration of the Vlasov equation in one spatial dimension based on a second order time-split algorithm with a local modified cubic-spline interpolation. We apply our approach to three different systems with long-range interactions: the Hamiltonian mean field, ring and self-gravitating sheet models. Speedups and accuracy for each model and different grid resolutions are presented.