The Discrete Element Method (DEM) is an efficient tool for modelling granular materials, usually approaching them by spherical particles. Aiming for a better description of grain shapes, the present work first illustrates the Level Set (LS) description of arbitrary surfaces in a DEM extension coined as LS-DEM. LS-DEM logically results in a massive increase in the simulation storage requirements and evaluation time, which is here illustrated with reference to DEM for the ideal case of spherical particles. Then, Level Set Quadtree/Octree data structures are proposed as algorithm improvements to alleviate the computational costs of LS-DEM.