Comparison of two Eulerian solvers for the four-dimensional Vlasov equation: Part I

This paper presents two methods for solving the four-dimensional Vlasov equation on a grid of the phase space. The two methods are based on the semi-Lagrangian method which consists in computing the distribution function at each grid point by following the characteristic curves ending there. The first method reconstructs the distribution function using local splines which are well suited for a parallel implementation. The second method is adaptive using wavelets interpolation: only a subset of the grid points are conserved to manage data locality. Numerical results are presented in the second part.