Cornerstone: Octree Construction Algorithms for Scalable Particle Simulations

TL;DR

Cornerstone introduces a scalable octree construction algorithm for particle simulations that efficiently operates on distributed HPC systems and GPUs, enabling large-scale N-body simulations with reduced data movement.

Contribution

The paper extends 3D graphics algorithms to HPC, providing a parallel, GPU-compatible octree construction method for scalable particle simulations.

Findings

Faster tree construction on CPUs and GPUs.

Supports large-scale simulations with up to 8 trillion particles.

Eliminates data movement between CPU and GPU memory.

Abstract

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.