Boosting Algorithmic Efficiency: Numerical Relativity in Dynamical, Curvilinear Coordinates

West Virginia University Research Corporation, Morgantown WV

Investigators

Abstract

Einstein's theory of general relativity (GR) provides science's current best understanding of gravity. It predicts the existence of bizarre objects like black holes and neutron stars, and ripples in spacetime called gravitational waves. These predictions motivated the construction of the Laser Interferometer Gravitational-wave Observatory (LIGO), which has detected several gravitational wave signals from colliding black holes and one signal from colliding neutron stars so far. For their efforts in making these detections possible, the leaders of LIGO were awarded the 2017 Nobel Prize in Physics. To obtain a deeper understanding about what produced the observed gravitational waves, LIGO data analysis compares observed waves with those predicted by Einstein's theory of GR for a very large number of possible scenarios. Construction of reliable theoretical models requires the full solutions to the equations underlying GR, provided by the field of numerical relativity. This project builds upon recent advances in this field to develop new software that greatly reduces the cost (in memory) of generating these solutions. Where before numerical relativity largely depended upon supercomputers, this new software will enable even consumer-grade desktop computers to generate needed theoretical predictions of merging black holes needed for LIGO data analysis. In the latter half of the funding period, the software will be made supercomputer-capable to enable (the far more memory-hungry) simulations of merging neutron stars on supercomputers with state-of-the-art accuracy. By unlocking the consumer-grade desktop as a powerful tool for numerical relativity, this project has the potential to enable the public to participate in the science in unprecedented ways. This will be made possible by incorporating this software into SETI@Home's "BOINC" volunteer computing infrastructure. The hope is that when LIGO detects a pair of merging black holes, thousands of black hole merger calculations will be launched for the benefit of LIGO science, each on a consumer-grade desktop computer running our "BlackHoles@Home" software. To educate the public and advertise this volunteer computing project both locally and globally, the West Virginia University group will give convocations in nearby high schools and write articles for the widely aggregated news site "The Conversation". Numerical relativity (NR) solves Einstein's equations of general relativity (GR), in full, on the computer. Improvements to the algorithmic and mathematical underpinnings of NR codes have recently culminated in a coming-of-age for the field, moving it beyond proof-of-principle calculations and into the realm of predictive astrophysics. Over the past two years, NR-based theoretical predictions of gravitational waves (GWs) were central to uncovering the binary parameters in LIGO's recent GW discoveries. Now that the age of multi-messenger astrophysics has arrived, physical scenarios involving gravitational field and magnetized fluid dynamics spanning orders of magnitude in length scale and timescale will need to be modeled. NR codes bridge these scales by dynamically adjusting their spatial numerical grids to better sample the space, but current algorithms do not account for near-symmetries in these systems or rely on complex mesh algorithms. The proposed project involves the development of a new NR code with the unique goal of being both algorithmically simple and highly efficient, minimizing computational and human effort while maximizing scientific impact. We call it SENR, the Simple, Efficient NR code. SENR is unique in its aim to perform NR simulations of compact binary inspirals atop a single, dynamical, bispherical-like spatial grid. Exploiting near-symmetries in the underlying system can reduce computational cost over the most widely-adopted NR methods by orders of magnitude, and minimizing the grid management infrastructure greatly simplifies the interpretation of numerical errors and the addition of new physics modules. SENR builds on a new, highly-robust approach in NR for solving the GR field equations with hydrodynamics on static curvilinear spatial grids with coordinate singularities (e.g., spherical polar coordinates), and the PI's team is extending the approach to arbitrary, dynamical coordinate systems. Development of SENR is accelerated by a Python-based code-generation tool developed for this project called NRPy+. Following best-practices in software design, the small SENR codebase is carefully optimized after each major feature is added to maximize scientific impact. SENR's memory efficiency unlocks the desktop as a tool for NR, enabling us to launch the first major volunteer computing effort to generate an enormous NR-based GW catalog for binary black holes. Further, SENR's scalability will enable us to leverage supercomputing resources to generate a very large double neutron star GW catalog as well. Simplicity in infrastructure greatly reduces effort required to add new physics modules, and we plan to incorporate Monte-Carlo-based photon and neutrino feedback to enable state-of-the-art realism in our compact binary simulations. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.