We investigate a hybrid numerical algorithm aimed at large-scale cosmological N-body simulation for on-going and future high precision sky surveys. It makes use of a truncated Fast Multiple Method (FMM) for short-range gravity, incorporating a Particle Mesh (PM) method for long-range potential, which is applied to deal with extremely large particle number. In this work, we present a specific strategy to modify a conventional FMM by a Gaussian shaped factor and provide quantitative expressions for the interaction kernels between multipole expansions. Moreover, a proper Multipole Acceptance Criterion for the hybrid method is introduced to solve potential precision loss induced by the truncation. Such procedures reduce the amount of computation compared to an original FMM and decouple the global communication. A simplified version of code is introduced to verify the hybrid algorithm, accuracy and parallel implementation.

我们研究了一种针对大规模宇宙学N的混合数值算法- 用于正在进行和未来的高精度天空测量的人体模拟。它利用截断快速多重方法（FMM）处理短程重力，结合粒子网格（PM）方法处理长程势，用于处理极大数量的粒子。在这项工作中，我们提出了一种通过高斯形状因子修改传统 FMM 的特定策略，并为多极展开之间的相互作用核提供定量表达式。此外，引入了混合方法的适当多极接受准则，以解决截断引起的潜在精度损失。与原始 FMM 相比，此类过程减少了计算量，并解耦了全局通信。引入了简化版本的代码来验证混合算法、准确性和并行实现。