ICE-COLA: fast simulations for weak lensing observables
  Approximate methods to full N-body simulations provide a fast and accurate
solution to the development of mock catalogues for the modeling of galaxy
clustering observables. In this paper we extend ICE-COLA (Izard et al. 2016),
based on an optimized implementation of the approximate COLA method, to produce
weak lensing maps and halo catalogues in the light cone using an integrated and
self consistent approach. We show that despite the approximate dynamics, the
catalogues thus produced enable an accurate modeling of weak lensing
observables one decade beyond the characteristic scale where the growth becomes
non-linear. In particular, we compare ICE-COLA to the MICE-GC N-body simulation
for some fiducial cases representative of upcoming surveys and find that, for
sources at redshift $z=1$, their convergence power spectra agree to within one
percent up to high multipoles (i.e., of order $1000$). The corresponding shear
two point functions, $\xi_{+}$ and $\xi_{-}$, yield similar accuracy down to
$2$ and $20$ arcmin respectively, while tangential shear around a $z=0.5$ lens
sample is accurate down to $4$ arcmin. We show that such accuracy is stable
against an increased angular resolution of the weak lensing maps. Hence, this
opens the possibility of using approximate methods for the joint modeling of
galaxy clustering and weak lensing observables and their covariance in ongoing
and future galaxy surveys.
