Developing High Order Stable and Efficient Methods for Long Time Simulations of Gravitational Waveforms

University Of Massachusetts, Dartmouth, North Dartmouth MA

Investigators

Abstract

Gravitational waves were predicted by Einstein a century ago. Still, they had never been directly observed before the Nobel Prize-winning discovery of black hole and neutron star binary systems by the US-based Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors in 2015. This detection heralded a major scientific transformation in the gravitational wave astrophysics field, which led to an urgent need for advanced computational models that will play a critical role in the future success of LIGO and upcoming space-borne missions like Laser Interferometer Space Antenna. High-accuracy gravitational wave simulations are needed to produce the expected gravitational wave signal emitted from these systems over hundreds of thousands of orbital cycles, which are required to filter noisy data. The main objective of this project is to develop new computational techniques to accurately and efficiently simulate gravitational waves that will allow scientists to maximize the scientific output of current and future detectors. These efforts open a window into the universe and capture the interest of the general public as well as a younger generation of scientists. Previous research projects by the investigators have been discussed in the general media, and this work will continue to be successful in outreach to the general public. The computational skills that the students develop are broadly applicable and, therefore, would allow them access to various career options, including in areas of urgent national need. The project aims to develop advanced mathematical and computational models to accurately simulate large-mass-ratio binary black hole systems, which are crucial for detecting gravitational waves. In particular, it will develop efficient and stable high-order methods that can handle the highly singular source terms of the s = ±2 Teukolsky model, including the development of a novel algorithm using a discontinuous Galerkin scheme and a mixed precision 2D weighted essentially non-oscillatory scheme. Work will also focus on developing high-order, positivity-preserving time-stepping methods with minimized phase and dispersion errors to enhance the accuracy of the simulations. The research outcomes will significantly impact the field of gravitational wave discoveries by enabling the modeling of highly realistic astrophysical scenarios that were previously infeasible, such as systems in which both black holes are rapidly spinning in the extreme mass ratio limit. 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.