A "metric" semi-Lagrangian Vlasov-Poisson solver

Understand

We propose a new semi-Lagrangian Vlasov-Poisson solver.

• It employs elements of metric to follow locally the flow and its deformation, allowing one to find quickly and accurately the initial phase-space position $Q(P)$ of any test particle $P$, by expanding at second order the geometry of the motion in the vicinity of the closest element.
• It is thus possible to reconstruct accurately the phase-space distribution function at any time $t$ and position $P$ by proper interpolation of initial conditions, following Liouville theorem.
• When distorsion of the elements of metric becomes too large, it is necessary to create new initial conditions along with isotropic elements and repeat the procedure again until next resampling.