Illustration of the different grids used within sCOLA. The Lagrangian lattice is represented by dashed lines. For each tile, central particles (in black) are surrounded by buffer particles (in cyan), which are ignored at the end of the evolution. The corresponding buffer region in other grids is represented in cyan. The left panel represents the “LPT grid” on which Lagrangian potentials and are defined. The central region has grid points (in red) and is padded by 2N_ghost cells in each direction (pink region). The right panel shows the “PM grid” on which the density contrast δ^sCOLA, the gravitational potential Φ^sCOLA, and the accelerations are defined. The density contrast is defined only in the central region (which has grid points, in dark green). The gravitational potential is padded by 2N_ghost cells in each direction (light green and yellow regions), and the gridded accelerations only by N_ghost cells in each direction (yellow region). Solving the Poisson equation requires Dirichlet boundary conditions in six layers of N_ghost cells, denoted as hatched regions. For simplicity of representation, we have used here N_ghost = 1.