SpaceHub: A high-performance gravity integration toolkit for few-body problems in astrophysics

TL;DR

SpaceHub is an open-source toolkit offering advanced algorithms for high-precision, fast, and accurate simulations of complex astrophysical few-body systems, outperforming existing methods in speed and accuracy.

Contribution

Introduction of novel algorithms AR-Radau, AR-Sym6, AR-ABITS, and AR-chain+ that outperform existing methods in precision and speed for astrophysical few-body problems.

Findings

AR-Sym6 and AR-chain+ are fastest and most accurate for black hole dynamics.

AR-Radau handles extremely eccentric orbits with high precision.

AR-ABITS achieves arbitrary precision with minimal CPU cost.

Abstract

We present the open source few-body gravity integration toolkit {\tt SpaceHub}. {\tt SpaceHub} offers a variety of algorithmic methods, including the unique algorithms AR-Radau, AR-Sym6, AR-ABITS and AR-chain$^+$ which we show out-perform other methods in the literature and allow for fast, precise and accurate computations to deal with few-body problems ranging from interacting black holes to planetary dynamics. We show that AR-Sym6 and AR-chain$^+$, with algorithmic regularization, chain algorithm, active round-off error compensation and a symplectic kernel implementation, are the fastest and most accurate algorithms to treat black hole dynamics with extreme mass ratios, extreme eccentricities and very close encounters. AR-Radau, the first regularized Radau integrator with round off error control down to 64 bits floating point machine precision, has the ability to handle extremely eccentric orbits and close approaches in long-term integrations. AR-ABITS, a bit efficient arbitrary precision method, achieves any precision with the least CPU cost compared to other open source arbitrary precision few-body codes. With the implementation of deep numerical and code optimization, these new algorithms in {\tt SpaceHub} prove superior to other popular high precision few-body codes in terms of performance, accuracy and speed.