A connected component-based method for efficiently integrating multiscale $N$-body systems

TL;DR

The paper introduces a new connected component-based method for efficiently simulating multiscale gravitational N-body systems, improving accuracy and computational performance in astrophysical simulations.

Contribution

It presents a novel recursive, adaptive partitioning approach using connected components and an explicit time step criterion, conserving momentum and enhancing efficiency.

Findings

Method outperforms existing integrators in numerical tests

Conserves linear and angular momentum to machine precision

Incorporated into the HUAYNO code within the AMUSE framework

Abstract

We present a novel method for efficient direct integration of gravitational N-body systems with a large variation in characteristic time scales. The method is based on a recursive and adaptive partitioning of the system based on the connected components of the graph generated by the particle distribution combined with an interaction-specific time step criterion. It uses an explicit and approximately time-symmetric time step criterion, and conserves linear and angular momentum to machine precision. In numerical tests on astrophysically relevant setups, the method compares favourably to both alternative Hamiltonian-splitting integrators as well as recently developed block time step-based GPU-accelerated Hermite codes. Our reference implementation is incorporated in the HUAYNO code, which is freely available as a part of the AMUSE framework.