  We present a detailed description and validation of our massively-parallel
update to the mass-Peak Patch method, a fully predictive initial-space
algorithm to quickly generate dark matter halo catalogues in very large
cosmological volumes. We perform an extensive systematic comparison to a suite
of N-body simulations covering a broad range of redshifts and simulation
resolutions, and find that, without any parameter fitting, our method is able
to generally reproduce N-body results while typically using over 3 orders of
magnitude less CPU time, and a fraction of the memory cost. Instead of
calculating the full non-linear gravitational collapse determined by an N-body
simulation, the mass-Peak Patch method finds an overcomplete set of
just-collapsed structures around a hierarchy of density-peak points by
coarse-grained (homogeneous) ellipsoidal dynamics. A complete set of
mass-peaks, or halos, is then determined by exclusion of overlapping patches,
and second order Lagrangian displacements are used to move the halos to their
final positions and to give their flow velocities. Our results show that the
mass-Peak Patch method is well-suited for creating large ensembles of halo
catalogues to mock cosmological surveys, and to aid in complex statistical
interpretations of cosmological models.
