Treecode2: The Power of Pluralism. I. Static Tests

TL;DR

This paper introduces a novel oct-tree N-body simulation method that employs random shifts and rotations of the root cell to statistically restore invariance and improve force accuracy in static tests.

Contribution

It presents a new averaging technique for oct-tree N-body codes that enhances force accuracy and invariance properties without significant computational overhead.

Findings

Averaging over multiple root cell configurations improves force accuracy.

The method restores translational and rotational invariance statistically.

Static tests confirm the effectiveness of the averaging approach.

Abstract

I describe an `oct-tree' N-body code which randomly shifts, reorients, and resizes the root cell at each time step. Averaging over a plurality of root cell positions and orientations statistically restores translational and rotational invariance. The potentials and forces which result can be much more accurate than those obtained from a single force calculation. In this paper, the principle of averaging is tested on static configurations. The next paper will show how this technique can substantially improve global energy, momentum, and angular momentum conservation at a negligible computational cost.