SUPERBOX is a particle-mesh code that uses moving sub-grids to track and resolve high-density peaks in the particle distribution and a nearest grid point force-calculation scheme based on the second derivatives of the potential. The code implements a fast low-storage FFT-algorithm and allows a highly resolved treatment of interactions in clusters of galaxies, such as high-velocity encounters between elliptical galaxies and the tidal disruption of dwarf galaxies, as sub-grids follow the trajectories of individual galaxies. SUPERBOX is efficient in that the computational overhead is kept as slim as possible and is also memory efficient since it uses only one set of grids to treat galaxies in succession.