Numerical Relativity Simulations with the New Mesh Code

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This award supports research in relativity and relativistic astrophysics and it addresses the priority areas of NSF's "Windows on the Universe" Big Idea. The first direct detection of gravitational waves emitted from merging black holes, by the NSF's LIGO detectors, was a historic breakthrough in gravitational physics, and led to the Noble prize in physics in 2017. Equally stunning was the detection of both gravitational waves and signal across the electromagnetic spectrum from gamma rays to radio waves, from the inspiral and merger of two neutron stars. With these and numerous subsequent similar detections a new window to the universe has been opened. More detections from a variety of other astrophysical sources are also anticipated. This project aims at making predictions about compact objects such as black holes and neutron stars, by running numerical simulations of the basic equations that govern such very dense and exotic objects. For this purpose a new computer program called Nmesh is being developed. Nmesh will be run on large scale supercomputers that nowadays consist of millions of compute cores. Making full and efficient use of so many cores involves various advanced programming techniques to run Nmesh in parallel. While the primary and immediate scientific goal of this project is the simulation of black holes and neutron stars, Nmesh can also be used to simulate other types of equations. Once it is well tested, Nmesh will be made publicly available. This will directly benefit other researchers in the area of numerical relativity, but since Nmesh is quite general it should also benefit others that need to solve different problems that are governed by different equations. Part of the research will be carried out in close collaboration with the relativity group at the University of Jena in Germany. Visits by faculty and students from both institutions are planned. This exchange will have educational benefits for students from both Florida Atlantic University (FAU) and the University of Jena.This project mainly focuses on binaries made up of black holes or neutron stars. When the two objects get close, fully non-linear numerical simulations of the Einstein equations are required to make predictions about the final part of the inspiral and subsequent merger. The project is aimed at gaining a detailed understanding of such compact-object binary inspirals and mergers by performing numerical simulations. Using the Nmesh program it will provide gravitational waveform catalogs, as well as information about ejecta when matter is involved. To achieve high accuracy results it is thus planned to further develop and upgrade Nmesh. This will enable the study of high mass ratio black hole inspirals, as well as binary neutron star simulations with improved accuracy. The results will also be used to improve and calibrate analytical waveform models to predict gravitational waves without needing to perform expensive numerical simulations. The upgrades to Nmesh will not only include advanced parallelization methods, but will also include the development of methods to treat shocks, within the framework of discontinuous Galerkin methods. The latter method is still new in numerical relativity, and thus requires special attention.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.