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We introduce FastPM, a highly-scalable approximated particle mesh N-bodysolver, which implements the particle mesh (PM) scheme enforcing correct lineardisplacement (1LPT) evolution via modified kick and drift factors. Employing a2-dimensional domain decomposing scheme, FastPM scales extremely well with avery 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 withdifferent number of steps ($N_s$) and force resolution factor ($B$) against 3benchmarks: halo mass function from Friends of Friends halo finder, halo anddark matter power spectrum, and cross correlation coefficient (orstochasticity), relative to a high resolution TreePM simulation. We show thatthe modified time stepping scheme reduces the halo stochasticity when comparedto 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 (afactor of 10) of computing time relative to $N_s=40$, $B=3$ simulation, yet thehalo benchmarks are very similar at $z=0$. We find that for abundance matchedhalos the stochasticity remains low even for $N_s=5$. FastPM compares wellagainst less expensive schemes, being only 7 (4) times more expensive than 2LPTinitial condition generator for $N_s=10$ ($N_s=5$). Some of the applicationswhere FastPM can be useful are generating a large number of mocks, producingnon-linear statistics where one varies a large number of nuisance orcosmological parameters, or serving as part of an initial conditions solver.

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