Tree codes and sort-and-sweep algorithms for neighborhood computation: A cache-conscious comparison

TL;DR

This paper compares cache-conscious sort-and-sweep and tree-code neighborhood algorithms in 2D DEM simulations, highlighting performance differences, system size effects, and parallelization potential.

Contribution

It provides a detailed comparison of two neighborhood algorithms in DEM, emphasizing cache efficiency and parallelization trade-offs.

Findings

Tree code has slightly better performance than sort-and-sweep.

Tree code increases cyclomatic complexity significantly.

Shared memory parallelization is more feasible with tree code.

Abstract

Neighborhood algorithms may take a considerable percentage of computer time in discrete element methods (DEM). While the sort-and-sweep algorithm is ideal in some ways, as it only deal with particles whose relative positions change in one coordinate direction, the other directions must be processed too, for all particles. In contrast, tree-codes deal only with adjacent particles. We compare sort-and-sweep and tree-code neighborhood algorithms for two-dimensional DEM simulations of polygonal particles in a rotating drum with up to 12000 particles. We discuss the effects of system size and inlining on the performance with respect to the cache memory. For the tree code, the performance is slightly better, at the cost of significantly increased cyclomatic complexity. In particular, one benefit is improved possibilities for shared memory parallelization.