Performance optimization of GJK collision detection in discrete element simulations

Abstract

This paper presents a comprehensive performance analysis of the Gilbert-Johnson-Keerthi (GJK) algorithm and its variants in the context of Discrete Element Method (DEM) simulations. Various optimization techniques, including bounding volumes, different distance sub-algorithms, Nesterov acceleration, and temporal coherence are investigated to evaluate their impact on computational efficiency for different particle shapes and aspect ratios. The study considers both static packing and rotating drum benchmarks, covering a wide range of particle geometries such as cubes, icosahedrons, cylinders, and superquadrics. Our findings indicate that the choice of bounding volume technique significantly affects performance, with oriented bounding cylinder outperforming oriented bounding boxes for elongated particles. Nesterov acceleration, although theoretically promising, generally shows limited performance improvements except for highly spherical particles. Temporal coherence, while beneficial for certain particle shapes and moderate aspect ratios, is less effective when particles are highly elongated or distant from each other. These results offer valuable insights for optimizing DEM simulations involving complex particle shapes and varying elongation levels.