NRPyElliptic

NRPyElliptic [Assumpcao et. al., PhysRevD.105.104037] (also [arXiv:gr-qc/2111.02424]) is a new, extensible elliptic solver that sets up initial data (ID) for numerical relativity (NR) using the same numerical methods employed for solving hyperbolic evolution equations. Specifically, NRPyElliptic implements the hyperbolic relaxation method of [Rüter et. al., arXiv:gr-qc/1708.07358] to solve complex nonlinear elliptic PDEs for NR ID. The hyperbolic PDEs are evolved forward in (pseudo)time, resulting in an exponential relaxation of the arbitrary initial guess to a steady state that coincides with the solution of the elliptic system. NRPyElliptic solves these equations on highly efficient numerical grids exploiting underlying symmetries in the physical scenario. To this end, NRPyElliptic is built within the SymPy-based NRPy+ framework, which facilitates the solution of hyperbolic PDEs on Cartesian-like, spherical-like, cylindrical-like, or bispherical-like numerical grids. For the purposes of setting up BBH puncture ID, NRPyElliptic makes use of the latter.

This repository hosts the following:

Tutorial-NRPyElliptic_BasicEquations.ipynb: documents the hyperbolized Hamiltonian constraint equation under the CTT formalism

Tutorial-Start_to_Finish-NRPyElliptic.ipynb: documents the C code generation for the standalone version of NRPyElliptic

NRPyElliptic_codegen: NRPy+-based code

Several NRPy+files (with minor modifications that will be incorporated into the main NRPy+ repository in the near future)

NRPyElliptic_Ccodes: trusted C code directory for the standalone version

NRPyEllipticET: Einstein Toolkit thorn based on the standalone version

Citation:

Thiago Assumpção, Leonardo R. Werneck, Terrence Pierre Jacques, and Zachariah B. Etienne. Fast hyperbolic relaxation elliptic solver for numerical relativity: Conformally flat, binary puncture initial data. Phys. Rev. D 105, 104037, 2022 (doi:10.1103/PhysRevD.105.104037)