Implementation of multi-grid Poisson solver in numerical relativity and its application to gravitational collapse of massive star

We develop a new grid-based multi-grid Poisson solver in numerical relativity. We report the performance of the multi-grid Poisson solver in the initial value problems for two-puncture black holes, a static spherical neutron star, a uniformly rotating neutron star in equilibrium, and a gravitationally collapsing massive star. As a demonstration, we conduct a numerical-relativity neutrino-radiation-transfer hydrodynamics simulation of the gravitational collapse of the $9M_{\odot }$ massive star in Ref.~\cite{Aguilera-Dena:2020mfh} up to the core bounce. During the simulation, we employ the constraint-preserving regird prescription with the newly developed multi-grid Poisson solver to improve the resolution. It shows that the baryonic mass, the Arnowit-Deser-Misner (ADM) mass, and the ADM-like angular momentum are, respectively, preserved with $O({10}^{-3})\mathrm{\%}$ and $O({10}^{-2})$–$O({10}^{-1})$% accuracy.