NRPyElliptic: A Fast Hyperbolic Relaxation Elliptic Solver for Numerical Relativity, I: Conformally Flat, Binary Puncture Initial Data

Abstract

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 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-wavespeed approach. While it is still $\sim 12$x slower than TwoPunctures at setting up full-3D BBH ID, NRPyElliptic requires only $\approx 0.3\%$ 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 star.

arXiv comment15 pages, 10 figures. Matches published version

References in corpus (48)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• On the Numerical Integration of Einstein's Field Equations
• Evolutions in 3D numerical relativity using fixed mesh refinement
• The Einstein Toolkit: A Community Computational Infrastructure for Relativistic Astrophysics
• Gauge conditions for long-term numerical black hole evolutions without excision
• A simple construction of initial data for multiple black holes
• Numerical Relativity Using a Generalized Harmonic Decomposition
• A single-domain spectral method for black hole puncture data
• A Fast Apparent-Horizon Finder for 3-Dimensional Cartesian Grids in Numerical Relativity
• Conformal ``thin sandwich'' data for the initial-value problem of general relativity
• Introduction to Isolated Horizons in Numerical Relativity
• Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. I. Method and tests
• Conformal and covariant formulation of the Z4 system with constraint-violation damping
• Constraint violation in free evolution schemes: comparing BSSNOK with a conformal decomposition of Z4
• Initial Data for Numerical Relativity
• A multidomain spectral method for solving elliptic equations
• Turduckening black holes: an analytical and computational study
• GWTC-2.1: Deep Extended Catalog of Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run
• General-covariant evolution formalism for Numerical Relativity
• High accuracy binary black hole simulations with an extended wave zone
• Kranc: a Mathematica application to generate numerical codes for tensorial evolution equations
• Binary Neutron Stars with Generic Spin, Eccentricity, Mass ratio, and Compactness - Quasi-equilibrium Sequences and First Evolutions
• Kadath: a spectral solver for theoretical physics
• Initial data for black hole-neutron star binaries: a flexible, high-accuracy spectral method
• Accurate gravitational waveforms for binary-black-hole mergers with nearly extremal spins
• Constraint damping of the conformal and covariant formulation of the Z4 system in simulations of binary neutron stars
• Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. III. Identical and different mass stars with gamma=2
• A new public code for initial data of unequal-mass, spinning compact-object binaries
• Accurate and realistic initial data for black hole-neutron star binaries
• SENR/NRPy+: Numerical Relativity in Singular Curvilinear Coordinate Systems
• Time Step Size Limitation Introduced by the BSSN Gamma Driver
• Binary Neutron Stars with Arbitrary Spins in Numerical Relativity
• Conformal Thin-Sandwich Solver for Generic Initial Data
• Non-conformally flat initial data for binary compact objects
• Improvements to the construction of binary black hole initial data
• Constructing Binary Neutron Star Initial Data with High Spins, High Compactness, and High Mass-Ratios
• A new code for equilibriums and quasiequilibrium initial data of compact objects
• Initial data for binary neutron stars with adjustable eccentricity
• Construction of initial data for 3+1 numerical relativity
• The initial value problem as it relates to numerical relativity
• Fully covariant and conformal formulation of the Z4 system in a reference-metric approach: comparison with the BSSN formulation in spherical symmetry
• Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. II. Newtonian limits
• Numerical method for binary black hole/neutron star initial data: Code test
• Illustrating Stability Properties of Numerical Relativity in Electrodynamics
• Hyperbolic Relaxation Method for Elliptic Equations
• A scalable elliptic solver with task-based parallelism for the SpECTRE numerical relativity code
• Initial data for black hole-neutron star binaries, with rotating stars
• Rio: A new computational framework for accurate initial data of binary black holes

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