Discrete element method simulations of super-quadric shaped particles have been performed by describing the particles using either a continuous function representation (CFR) or as an array of discrete points (discrete function representation, DFR). For the DFR, techniques of uniform discretization and adaptive discretization were proposed for spherical and non-spherical particles, respectively. The concept of a 'contact candidate list' was put forward to speed up the stage of contact detection. For the CFR, a numerical approach was described to determine the contact point between colliding particles. Points generated through the DFR were used to make the initial guess for the numerical, Newton-Raphson based iterations. The proposed algorithms were employed to model hoppers, horizontal rotating cylinders and vibrated beds. By analyzing the dynamics of these systems the number of discrete points required accurately to describe particles using the DFR was determined. The efficiencies of the DFR and the CFR were measured based on the system of a horizontal rotating cylinder. The characteristics of both modeling approaches in granular simulations were highlighted. (C) 2012 Elsevier Ltd. All rights reserved.