The Level Set-Discrete Element Method (LS-DEM) extends DEM towards abitrary grain shapes by storing distance-to-surface values on a grid for each Discrete Element (DE), together with considering boundary nodes located onto,the DE’s surface. Both these ingredients are shown to affect the precision and computational costs of LS-DEM, considering various numerical simulations at the contact- and packing-scales for ideal spherical and superellipsoid shapes. In the case of a triaxial compression for spherical particles, approaching with a reasonable precision the reference result obtained in classical DEM requires the grid spacing to be smaller than one tenth of particle size, as well as using a couple thousands of boundary nodes. Computational costs in terms of memory (RAM) or evaluation time then increase in LS-DEM by two or three orders of magnitude. Simple OpenMP parallel simulations nevertheless significantly reduce the increase in time cost, possibly dividing the latter by 20.