The H.E.S.S. gravitational wave rapid follow-up program

Gravitational Wave (GW) events are physical processes that significantly perturbate space-time, e.g. compact binary coalescenses, causing the production of GWs. The detection GWs by a worldwide network advanced interferometers offer unique opportunities for multi-messenger searches and electromagnetic counterpart associations. While carrying extremely useful information, associated emission challenging due to large sky localisation uncertainties provided current GW observatories LIGO Virgo. Here we present methods procedures used within High Energy Stereoscopic System (H.E.S.S.) in very-high-energy (VHE) gamma-ray from extreme events. To do so create several algorithms dedicated schedule follow-up observations creating optimized pointing paterns. We describe using 2-dimensional information correlating galaxy distribution local universe, catalogs, with 3-dimensional evaluate their performances. H.E.S.S. automatic chain, described this paper, is initiate less than 1 minute after alert reception. These developements allowed 6 out 67 non-retracted detected during first three observation runs Virgo reaching VHE $\gamma$-ray coverages up 70% localisation.