  We present sCOLA -- an extension of the N-body COmoving Lagrangian
Acceleration (COLA) method to the spatial domain. Similar to the original
temporal-domain COLA, sCOLA is an N-body method for solving for large-scale
structure in a frame that is comoving with observers following trajectories
calculated in Lagrangian Perturbation Theory. Incorporating the sCOLA method in
an N-body code allows one to gain computational speed by capturing the
gravitational potential from the far field using perturbative techniques, while
letting the N-body code solve only for the near field. The far and near fields
are completely decoupled, effectively localizing gravity for the N-body side of
the code. Thus, running an N-body code for a small simulation volume using
sCOLA can reproduce the results of a standard N-body run for the same small
volume embedded inside a much larger simulation. We demonstrate that sCOLA can
be safely combined with the original temporal-domain COLA. sCOLA can be used as
a method for performing zoom-in simulations. It also allows N-body codes to be
made embarrassingly parallel, thus allowing for efficiently tiling a volume of
interest using grid computing. Moreover, sCOLA can be useful for cheaply
generating large ensembles of accurate mock halo catalogs required to study
galaxy clustering. Surveys that will benefit the most are ones with large
aspect ratios, such as pencil-beam surveys, where sCOLA can easily capture the
effects of large-scale transverse modes without the need to substantially
increase the simulated volume. As an illustration of the method, we present
proof-of-concept zoom-in simulations using a freely available sCOLA-based
N-body code.
