# A Very Fast And Angular Momentum Conserving Tree Code

## TL;DR

This paper presents a modification to the Cartesian fast multipole method that ensures conservation of both angular and linear momentum in astrophysical gravitational simulations, improving accuracy over traditional methods.

## Contribution

The authors introduce a novel modification to the fast multipole method that guarantees conservation of angular momentum, a feature not present in previous implementations.

## Key findings

- The modified tree code conserves angular momentum to machine precision.
- Linear momentum conservation is maintained alongside angular momentum.
- The method is efficient and applicable to astrophysical simulations.

## Abstract

There are many methods used to compute the classical gravitational field in astrophysical simulation codes. With the exception of the typically impractical method of direct computation, none ensure conservation of angular momentum to machine precision. Under uniform time-stepping, the Cartesian fast multipole method of Dehnen (also known as the very fast tree code) conserves linear momentum to machine precision. We show it is possible to modify this method in a way that conserves both angular and linear momenta.