Topics in Numerical Relativity: Horizon Finding, Asynchronous Parallelism, and Cross-Code Comparisons of Gravitational Waveforms

Author: Nelli, Kyle Christopher

Year: 2026

Degree: Dissertation (Ph.D.)

Advisor: Teukolsky, Saul A.

Committee Members: Chatziioannou, Katerina; Scheel, Mark; Teukolsky, Saul A.; Bouman, Katherine L.

Option: Physics

Abstract

From their prediction in 1916 by Einstein, to their first detection almost 100 years later in 2015, gravitational waves provide a new way of looking at the universe, completely separate from electromagnetic radiation. They allow us to probe and study the most extreme gravitational environments that our universe has to offer; black holes. When two black holes merge, they produce a burst of gravitational waves which, if energetic enough, are able to be detected here on earth.

However, to effectively model these mergers, we cannot solely rely on analytical descriptions. They break down near the actual merger, when spacetime is at its most extreme. To model this merger, we need numerical simulations of mergers to predict what they will look like. These simulations must be extremely accurate due to the incredible precision with which we are able to detect gravitational waves. Therefore, these expensive simulations need to run on supercomputers and be highly efficient in order to meet the necessary accuracy requirements.

In this thesis, we present a novel algorithm for efficiently finding the apparent horizons in numerical simulations done with task-based parallelism. The performance improvement of task-based parallelism over more traditional parallelism is significant, but it introduces considerable algorithmic complexity which had to be dealt with. We then use this novel algorithm to perform the first binary black hole merger done with discontinuous Galerkin methods and analyze the waveform output. Lastly, we present a new feature to the SpECTRE CCE module which allows it to be run on data from other numerical relativity codes. We show this new feature working on simulation data from five different numerical relativity codes.