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Resolving numerically Vlasov-Poisson equations for initially cold systems canbe reduced to following the evolution of a three-dimensional sheet evolving insix-dimensional phase-space. We describe a public parallel numerical algorithmconsisting in representing the phase-space sheet with a conforming,self-adaptive simplicial tessellation of which the vertices follow theLagrangian equations of motion. The algorithm is implemented both in six- andfour-dimensional phase-space. Refinement of the tessellation mesh is performedusing the bisection method and a local representation of the phase-space sheetat 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\'einvariants. Resolution of Poisson equation is performed using the fast Fouriermethod on a regular rectangular grid, similarly to particle in cells codes. Tocompute the density projected onto this grid, the intersection of thetessellation and the grid is calculated using the method of Franklin andKankanhalli (1993) generalised to linear order. As preliminary tests of thecode, we study in four dimensional phase-space the evolution of an initiallysmall patch in a chaotic potential and the cosmological collapse of afluctuation composed of two sinusoidal waves. We also perform a "warm" darkmatter simulation in six-dimensional phase-space that we use to check theparallel scaling of the code.

ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation