Vlasov simulations on an adaptive phase-space grid

We introduce here a new method for the numerical resolution of the Vlasov equation on a phase space grid using an adaptive semi-Lagrangian method. The adaptivity is obtained through a multiresolution analysis which enables to keep or remove grid points from the simulation depending on the size of their associated coefficients in a multiresolution expansion. The adaptive algorithm consists in three steps : prediction of the active grid points at the next time step, the usual semi-Lagrangian algorithm, and a compression allowing to eliminate unnecessary grid points.