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 numerical domain, similar to the widely used TwoPunctures code. Unlike TwoPunctures, NRPyElliptic employs a hyperbolic relaxation scheme, whereby arbitrary elliptic partial differential equations (PDEs) are trivially transformed into a hyperbolic system of PDEs. As consumers of NR ID generally already possess expertise in solving hyperbolic PDEs, they will generally find NRPyElliptic easier to tweak and extend than other NR elliptic solvers. When evolved forward in (pseudo)time, the hyperbolic system exponentially reaches a steady state that solves the elliptic PDEs. Notably NRPyElliptic accelerates the relaxation waves, which makes it many orders of magnitude faster than the usual constant wave speed approach. While it is still ???12x slower than TwoPunctures at setting up full-3D BBH ID, NRPyElliptic requires only ???0.3% of the runtime for a full BBH simulation in the Einstein Toolkit. Future work will focus on improving performance and generating other types of ID, such as binary neutron stars.

Automated summary

NRPyElliptic is an elliptic solver built within the NRPy+ framework for numerical relativity. Unlike other solvers, it employs a hyperbolic relaxation scheme, making it easier to tweak and extend. It accelerates the relaxation waves and is much faster than the constant wave speed approach. Although slower in setting up initial data, it is very fast in full simulations.