Fast hyperbolic relaxation elliptic solver for numerical relativity: Conformally flat, binary puncture initial data

We introduce NRPyElliptic, an elliptic solver for numerical relativity (NR) built within the NRPy+ framework. As its first application, NRPyElliptic sets up conformally flat, binary black hole (BBH) puncture initial data (ID) on a single domain, similar to widely used TwoPunctures code. Unlike TwoPunctures, employs hyperbolic relaxation scheme, whereby arbitrary PDEs are trivially transformed into system of PDEs. consumers NR ID generally already possess expertise in solving PDEs, they will find easier tweak and extend than other solvers. When evolved forward (pseudo)time, exponentially reaches steady state that solves Notably accelerates waves, which makes it many orders magnitude faster usual constant-wavespeed approach. While is still ${\sim}12$x slower at setting full-3D BBH ID, requires only ${\approx}0.3\%$ runtime full simulation Einstein Toolkit. Future work focus improving performance generating types such as neutron star.