标题： 核心：可扩展粒子模拟的八叉树构建算法 显示英文标题

标题： Cornerstone: Octree Construction Algorithms for Scalable Particle Simulations

摘要： 本文提出了一种八叉树构建方法，称为Cornerstone，该方法有助于在无网格数值模拟中进行全局域分解和粒子间的相互作用。 我们的方法基于为3D计算机图形学开发的算法，并将其扩展到分布式高性能计算（HPC）系统。 Cornerstone生成全局和局部必要的八叉树，并能够在所有树层次结构上并行操作。 生成的八叉树适用于支持N体方法中各种短程和长程相互作用的计算，例如Barnes-Hut和快速多极子方法（FMM）。 虽然我们提供了CPU实现，但Cornerstone可以在GPU上完全运行。 这相比在CPU上执行显著加快了树的构建，并作为设计超越卸载方法的模拟代码的强大构建模块，其中只有数值密集型任务被发送到GPU。 由于数据仅存在于GPU内存中，Cornerstone消除了CPU和GPU之间的数据移动。 作为示例，我们使用Cornerstone为在几乎完整的LUMI-G系统上运行的Barnes-Hut树代码生成局部必要的八叉树，最多支持8万亿个粒子。 显示英文摘要

摘要： This paper presents an octree construction method, called Cornerstone, that facilitates global domain decomposition and interactions between particles in mesh-free numerical simulations. Our method is based on algorithms developed for 3D computer graphics, which we extend to distributed high performance computing (HPC) systems. Cornerstone yields global and locally essential octrees and is able to operate on all levels of tree hierarchies in parallel. The resulting octrees are suitable for supporting the computation of various kinds of short and long range interactions in N-body methods, such as Barnes-Hut and the Fast Multipole Method (FMM). While we provide a CPU implementation, Cornerstone may run entirely on GPUs. This results in significantly faster tree construction compared to execution on CPUs and serves as a powerful building block for the design of simulation codes that move beyond an offloading approach, where only numerically intensive tasks are dispatched to GPUs. With data residing exclusively in GPU memory, Cornerstone eliminates data movements between CPUs and GPUs. As an example, we employ Cornerstone to generate locally essential octrees for a Barnes-Hut treecode running on almost the full LUMI-G system with up to 8 trillion particles.