This talk describes the DEM algorithms and heuristics that are optimized for the parallel NVIDIA® Kepler GPU architecture in detail. This includes a novel collision detection algorithm for convex polyhedra based on the separating plane (SP) method. In addition, we present heuristics optimized for the parallel NVIDIA® Kepler GPU architecture. Our algorithms have minimalistic memory requirements, which enables us to store data in the limited but high bandwidth constant memory on the GPU. We then systematically verify the DEM implementation after we demonstrate the computational scaling on two large-scale simulations.