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

求解爱因斯坦方程的计算方法的发展是由目前部署的引力波探测器推动的，如地面LIGO和未来的天基LISA。为了充分理解和分析用这种设备测量的信号和波形，必须有准确、健壮和高效的计算工具来求解很长时间尺度上的爱因斯坦方程。由该奖项支持的研究将继续由加州理工大学-康奈尔数值相对论合作开发光谱爱因斯坦代码。谱方法的高精度和高效率可以在比现有有限差分代码更长的时间尺度上进行模拟，并可以提供使用现有计算机硬件进行LIGO和LISA数据分析所需的额外精度。这项研究将对我们对基础物理的理解产生广泛影响，特别是测试像黑洞这样的强场情况下的广义相对论。此外，它还将对更广泛的计算科学领域产生重大影响。所涉及的计算技术可以用于解决许多其他领域的问题，包括流体动力学、气象学、地震学和天体物理学。受过这些技术培训的年轻研究人员需求量很大。

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.