The next big step in gravitational-wave science is going to be the construction of next-generation detectors like LISA, CE, and ET. These detectors will detect signals with much higher accuracy, which means the numerical relativity waveforms used to build and calibrate various gravitational-wave models will also need to improve. This thesis is about pushing our code, SpEC, as far as possible to see how accurate we can get, and fixing issues that might prevent us from reaching the accuracy required by the next generation of detectors. In this thesis, I highlight two improvements made to SpEC with this goal in mind. First, I describe work that makes the black hole spin calculations much faster. The spin calculations were becoming very slow near the merger, when the horizons were highly deformed, and they would only get worse as we increased the resolution of our simulations. The new algorithm is much faster and also opens up paths to future improvements if required. Second, I study various sources of errors in SpEC binary black hole simulations and how to reduce them. We find that relatively targeted changes can improve waveform accuracy by around two orders of magnitude without significantly increasing simulation cost. We also identify some more fundamental limitations that should be considered as we do more high-resolution simulations. Finally, I show preliminary results from an ongoing project demonstrating that, for simple systems, the improvements discussed in this thesis can reach the accuracy required by LISA. Together, these results show that SpEC can be pushed much further than the current catalog simulations. They also provide a clearer path to producing high-accuracy numerical relativity waveforms needed for LISA and other next-generation gravitational-wave detectors.
Himanshu Chaudhary (Thu,) studied this question.