FastPM: a new scheme for fast simulations of dark matter and haloes

We introduce FASTPM, a highly scalable approximated particle mesh (PM) N-body solver, which implements the PM scheme enforcing correct linear displacement (1LPT) evolution via modified kick and drift factors. Employing a two-dimensional domain decomposing scheme, FASTPM scales extremely well with a very large number of CPUs. In contrast to Comoving-Lagrangian (COLA) approach, we do not require to split the force or track separately the 2LPT solution, reducing the code complexity and memory requirements. We compare FASTPM with different number of steps (N_s) and force resolution factor (B) against three benchmarks: halo mass function from friends-of-friends halo finder; halo and dark matter power spectrum; and cross-correlation coefficient (or stochasticity), relative to a high-resolution TREEPM simulation. We show that the modified time stepping scheme reduces the halo stochasticity when compared to COLA with the same number of steps and force resolution. While increasing N_s and B improves the transfer function and cross-correlation coefficient, for many applications FASTPM achieves sufficient accuracy at low N_s and B. For example, N_s = 10 and B = 2 simulation provides a substantial saving (a factor of 10) of computing time relative to N_s = 40, B = 3 simulation, yet the halo benchmarks are very similar at z = 0. We find that for abundance matched haloes the stochasticity remains low even for N_s = 5. FASTPM compares well against less expensive schemes, being only 7 (4) times more expensive than 2LPT initial condition generator for N_s = 10 (N_s = 5). Some of the applications where FASTPM can be useful are generating a large number of mocks, producing non-linear statistics where one varies a large number of nuisance or cosmological parameters, or serving as part of an initial conditions solver.