  We present the COmoving Lagrangian Acceleration (COLA) method: an N-body
method for solving for Large Scale Structure (LSS) in a frame that is comoving
with observers following trajectories calculated in Lagrangian Perturbation
Theory (LPT). Unlike standard N-body methods, the COLA method can
straightforwardly trade accuracy at small-scales in order to gain computational
speed without sacrificing accuracy at large scales. This is especially useful
for cheaply generating large ensembles of accurate mock halo catalogs required
to study galaxy clustering and weak lensing, as those catalogs are essential
for performing detailed error analysis for ongoing and future surveys of LSS.
As an illustration, we ran a COLA-based N-body code on a box of size 100Mpc/h
with particles of mass ~5*10^9Msolar/h. Running the code with only 10 timesteps
was sufficient to obtain an accurate description of halo statistics down to
halo masses of at least 10^11Msolar/h. This is only at a modest speed penalty
when compared to mocks obtained with LPT. A standard detailed N-body run is
orders of magnitude slower than our COLA-based code. The speed-up we obtain
with COLA is due to the fact that we calculate the large-scale dynamics exactly
using LPT, while letting the N-body code solve for the small scales, without
requiring it to capture exactly the internal dynamics of halos. Achieving a
similar level of accuracy in halo statistics without the COLA method requires
at least 3 times more timesteps than when COLA is employed.
