Assessing the Hierarchical Hamiltonian Splitting Integrator for Collisionless N-body Simulations

TL;DR

This paper evaluates the hierarchical Hamiltonian splitting (HHS) integrator for collisionless N-body simulations, demonstrating its advantages over traditional methods in terms of reversibility and energy conservation, especially for direct summation and P3M codes.

Contribution

The study provides a numerical assessment of HHS, showing it as a promising alternative to AKDK with better energy stability and potential benefits for advanced simulation codes.

Findings

HHS is approximately reversible unlike AKDK.

HHS achieves milder energy drift under optimal parameters.

HHS shows advantages in direct summation and P3M codes.

Abstract

The large dynamic range in some astrophysical N-body problems led to the use of adaptive multi-time-steps; however, the search for optimal strategies is still challenging. We numerically quantify the performance of the hierarchical Hamiltonian Splitting (HHS) integrator for collisionless simulations using a direct summation code. We compare HHS with the constant global time-step leapfrog integrator, and with the adaptive one (AKDK). We find that HHS is approximately reversible, whereas AKDK not. Therefore, it is possible to find a combination of parameters where the energy drift is considerably milder for HHS, resulting in a better performance. We conclude that HHS is an attractive alternative to AKDK, and it is certainly advantageous for direct summation and P3M codes. Also, we find advantages with GADGET4 (Tree/FMM) HHS implementation that are worth exploring further.