Afterlive: A performant code for Vlasov-Hybrid simulations

A parallelized implementation of the Vlasov-Hybrid method Nunn (1993) is presented. This method is a hybrid between a gridded Eulerian description and Lagrangian meta-particles. Unlike the Particle-in-Cell method Dawson (1983) which simply adds up the contribution of meta-particles, this method does a reconstruction of the distribution function f in every time step for each species. This interpolation method combines meta-particles with different weights in such a way that particles with large weight do not drown out particles that represent small contributions to the phase space density. These core properties allow the use of a much larger range of macro factors and can thus represent a much larger dynamic range in phase space density.

The reconstructed phase space density f is used to calculate momenta of the distribution function such as the charge density p. The charge density p is also used as input into a spectral solver that calculates the self-consistent electrostatic field which is used to update the particles for the next time-step.

Afterlive (AF ourier-based T ool in the E lectrostatic limit for the R apid L ow-noise I ntegration of the V lasov E quation) is fully parallelized using MPI and writes output using parallel HDF5. The input to the simulation is read from a JSON description that sets the initial particle distributions as well as domain size and discretization constraints. The implementation presented here is intentionally limited to one spatial dimension and resolves one or three dimensions in velocity space. Additional spatial dimensions can be added in a straight forward way, but make runs computationally even more costly.

本文提出了一种对 Nunn（1993）所提出的 Vlasov-Hybrid 方法进行并行化实现的方案。该方法介于网格化的欧拉描述与拉格朗日元粒子法之间。与简单叠加元粒子贡献的 Particle-in-Cell 方法（Dawson，1983）不同，此方法在每个时间步为每种粒子种类进行分布函数 f 的重建。该插值方法通过以不同权重结合元粒子，确保了权重较大的粒子不会淹没代表相空间密度小贡献的粒子。这些核心特性使得能够采用更广泛的宏观因素范围，从而在相空间密度上表征更广泛的动态范围。

重建的相空间密度 f 被用于计算分布函数的动量，如电荷密度 p。电荷密度 p 还被用作输入，进入一个光谱求解器，计算自洽静电场，该场用于更新下一时间步的粒子。

在静电极限下，基于傅里叶变换的 Afterlife（AF ourier-based T ool in the E lectrostatic limit for the R apid L ow-noise I ntegration of the V lasov E quation）工具被完全并行化，利用 MPI 进行并行处理，并使用并行 HDF5 编写输出。模拟的输入是从 JSON 描述中读取的，该描述设定了初始粒子分布、区域大小以及离散化约束。此处提出的实现故意限制在一维空间内，并解析速度空间中的一维或三维。可以通过直接方式添加额外的空间维度，但这会使计算成本进一步提高。