Algorithms, Scientific Computing, and Numerical Studies in Classical and Quantum General Relativity

将开发一套全面的新算法和科学计算工具，以更高的效率对双星黑洞碰撞的数学模型进行数值研究。将开发符号处理工具，使用量子场论的技术自动处理和获得爱因斯坦方程的高阶后牛顿展开。将探索在数值相对论中使用异质计算，更具体地说，是通用图形处理单元(GPU)。该项目中开发的工具旨在探索二元黑洞碰撞的物理，预计将成为LIGO和LISA等地面和空间干涉仪探测到的引力波的主要来源之一。参数空间如此之大，以至于需要新的计算范式来探索。这个项目的结果应该在广义相对论、引力波、符号计算代数、场论和高性能计算的广泛领域引起人们的兴趣。

A comprehensive set of new algorithmic and scientific computing tools to numerically investigate the modeling of binary black hole collisions with higher efficiency will be developed. Symbolic manipulation tools to automatize and obtain higher order post-Newtonian expansions of the Einstein equations using techniques from Quantum Field Theory will be developed.  The use of heterogeneous computing and, more specifically, general purpose Graphics Processing Units (GPUs) in numerical relativity will be explored. The tools developed in this project aim to explore the physics of binary black hole collisions, expected to be one of the main sources of gravitational waves to be detected by ground- and space-based interferometers such as LIGO and LISA. The parameter space is so large that new computing paradigms are needed to explore it. The results of this project should be of interest in the broad areas of general relativity, gravitational waves, symbolic computing algebra, field theory, and high performance computing.