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

The mass-Peak Patch algorithm for fast generation of deep all-sky dark matter halo catalogues and its N-Body validation