On Distributed Gravitational N-Body Simulations

TL;DR

This paper explores distributed and parallel algorithmic techniques to improve the scalability and efficiency of large-scale gravitational N-body simulations, focusing on reducing communication and enhancing parallelism.

Contribution

It introduces novel distributed and parallel variations of the Barnes-Hut algorithm with detailed implementation and evaluation on a multi-node cluster.

Findings

Improved scalability of N-body simulations on multi-node clusters.

Reduced inter-process communication in distributed algorithms.

Demonstrated effectiveness of techniques on a 10-node cluster.

Abstract

The N-body problem is a classic problem involving a system of N discrete bodies mutually interacting in a dynamical system. At any moment in time there are N*(N - 1)/2 such interactions occurring. This scaling as N^2 leads to computational difficulties where simulations range from tens of thousands of bodies to many millions. Approximation algorithms, such as the famous Barnes-Hut algorithm, simplify the number of interactions to scale as N(log N). Even still, this improvement in complexity is insufficient to achieve the desired performance for very large simulations on computing clusters with many nodes and many cores. In this work we explore a variety of algorithmic techniques for distributed and parallel variations on the Barnes-Hut algorithm to improve parallelism and reduce inter-process communication requirements. Explicit algorithms and details are provided for reproducibility. Our MPI implementation of distributed gravitational N-body simulation, freely available on GitHub, is evaluated on a cluster of 10 nodes, each with two 6-core CPUs, to test the effectiveness and scalability of the aforementioned techniques.