Zooming into Vlasov-Poisson using the characteristic mapping method

We propose an efficient semi-Lagrangian characteristic mapping method for solving the one+one-dimensional Vlasov-Poisson equations with high precision on a coarse grid. The flow map is evolved numerically with a gradient-augmented level-set method and exponential resolution in linear time is obtained. Global third order convergence in space and time is shown and conservation properties are assessed. For benchmarking we consider Landau damping and the two-stream instability. We compare the results with a classical pseudo-spectral method. The extreme fine-scale resolution features are illustrated with zooms showing the method's capabilities of going beyond the limit of currently available schemes.