  Resolving numerically Vlasov-Poisson equations for initially cold systems can
be reduced to following the evolution of a three-dimensional sheet evolving in
six-dimensional phase-space. We describe a public parallel numerical algorithm
consisting in representing the phase-space sheet with a conforming,
self-adaptive simplicial tessellation of which the vertices follow the
Lagrangian equations of motion. The algorithm is implemented both in six- and
four-dimensional phase-space. Refinement of the tessellation mesh is performed
using the bisection method and a local representation of the phase-space sheet
at second order relying on additional tracers created when needed at runtime.
In order to preserve in the best way the Hamiltonian nature of the system,
refinement is anisotropic and constrained by measurements of local Poincar\'e
invariants. Resolution of Poisson equation is performed using the fast Fourier
method on a regular rectangular grid, similarly to particle in cells codes. To
compute the density projected onto this grid, the intersection of the
tessellation and the grid is calculated using the method of Franklin and
Kankanhalli (1993) generalised to linear order. As preliminary tests of the
code, we study in four dimensional phase-space the evolution of an initially
small patch in a chaotic potential and the cosmological collapse of a
fluctuation composed of two sinusoidal waves. We also perform a "warm" dark
matter simulation in six-dimensional phase-space that we use to check the
parallel scaling of the code.
