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

TL;DR

ColDICE is a parallel, adaptive tessellation-based solver for Vlasov-Poisson equations that accurately tracks cold systems in high-dimensional phase-space, demonstrating good scalability and detailed phase-space evolution.

Contribution

This paper introduces a novel parallel algorithm using adaptive simplicial tessellation for solving Vlasov-Poisson equations in 4D and 6D phase-space, with improved refinement and Hamiltonian preservation.

Findings

Successfully simulates chaotic potential evolution in 4D phase-space.

Performs cosmological collapse simulations with high resolution.

Exhibits good parallel scaling in dark matter simulations.

Abstract

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.