Collaborative Research: Developing Spectral Methods for Numerical Solution of Einstein's Equations

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The development of computational methods for solving Einstein's equations is motivated by the current deployment of gravitational wave detectors such as the ground-based LIGO and the future space-based LISA. To fully understand and analyze the signals and waveforms measured with such facilities it is essential that accurate, robust, and efficient computational tools be available for solving Einstein's equations over very long time scales. The research supported by this award will continue the development of the Spectral Einstein Code by the Caltech-Cornell numerical relativity collaboration. The high accuracy and efficiency of spectral methods could allow simulations over longer timescales than existing finite difference codes and could provide the additional accuracy needed for aspects of LIGO and LISA data analysis using currently available computer hardware.This research will have a broad impact on our understanding of fundamental physics, in particular testing General Relativity for strong field situations like black holes. In addition, it will have a significant impact on the broader area of computational science. The computational techniques involved can be used to solve problems in many other areas, including fluid dynamics, meteorology, seismology, and astrophysics. Young researchers trained in these techniques are in great demand.