Tree Code Based Neighborhood Algorithms for Discrete Element Methods

TL;DR

This paper explores a tree-code based neighborhood algorithm for discrete element methods, demonstrating comparable or improved performance over traditional methods in 2D systems with several thousand particles.

Contribution

It introduces a tree-code implementation for DEM that achieves $N ext{log}N$ complexity, offering an alternative to existing sort and sweep methods.

Findings

Tree-code implementation achieves $N ext{log}N$ complexity.

Performance is slightly better than sort and sweep for certain conditions.

Algorithm is more complex than traditional methods.

Abstract

We report our experiences for the development of a neighborhood algorithm implemented via tree-codes to optimize the performance of a discrete element method (DEM) for convex polytopes. Our implementation of the two-dimensional tree code needs $N\log N$, as does the sort and sweep approach. For our choice of boundary conditions (a rotating drum) and system sizes (up to several thousand particles), the performance of the tree-code is slightly better, but the algorithm is considerably more complicated than the sort and sweep approach.