Enhancement of GJK-EPA Algorithm for Improved Contact Detection in Discrete Element Method Simulations

This study proposes several key improvements based on detailed analysis of the Minkowski difference. In the Gilbert–Johnson–Keerthi (GJK) algorithm, a stable orthogonal search direction is constructed at the midpoint of a line-segment simplex to eliminate zero-vector degeneracy, while the origin position relative to a triangular simplex is rapidly determined using the triangle normal. In the Expanding Polytope algorithms (EPA), the simplex is expanded directly along the triangular normal to form a tetrahedron. A novel outward normal vector determination method is also introduced using the vector between two non-coplanar tetrahedral vertices, resolving failures when the origin lies on a face. The improved GJK-EPA algorithm was implemented in a discrete element framework for gravitational stacking simulations of ellipsoidal–polyhedral particles. Validation against physical experiments showed excellent agreement, with an average repose angle difference of only 4.18° and a relative error in pile height of 4%. Large-scale polyhedral stacking simulations demonstrated denser packing structures with smoother surface profiles. Compared with the conventional GJK-EPA, the proposed algorithm reduces computational time by 13%, decreases the maximum number of iterations by up to three, and improves maximum contact depth accuracy by 8%. Although its contact depth accuracy is slightly lower than that of the GJK-EPA-IPM method, its computational time is only 52% of the latter. These results confirm that the improvements provide a superior balance between accuracy and efficiency for polyhedral particle simulations.