ColDICE：一个使用移动自适应单纯形细分的并行Vlasov-Poisson求解器
ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation
摘要：
解决数值Vlasov-Poisson方程的初始冷系统，可以减少到以下的三维片在六维相空间中演变的演变。我们描述了一个公共的并行数值算法，包括在相空间片与一个符合，自适应单纯形镶嵌的顶点遵循拉格朗日方程的运动。该算法在六维和四维相空间中实现。细化的镶嵌网格进行二分法和相空间表的本地表示在二阶依赖于额外的示踪剂时，需要在运行时创建。为了以最好的方式保持系统的哈密顿性质，细化是各向异性的，并受到局部庞加莱不变量的测量的约束。泊松方程的解决方案是使用快速傅立叶方法在一个规则的矩形网格，类似于粒子在细胞的代码。为了计算投影到该网格上的密度，使用Franklin和Kankanhalli（1993）推广到线性顺序的方法计算镶嵌和网格的交点。作为程序的初步测试，我们在四维相空间中研究了混沌势中初始小块的演化和由两个正弦波组成的涨落的宇宙学坍缩。我们还进行了一个“温暖”的暗物质模拟在六维相空间，我们用来检查并行缩放的代码。
英文摘要：
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 Poincaré 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.
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