FRG: Collaborative Research: Developing Spectral Methods for Numerical Solutions of the Einstein Equations

FRG：合作研究：开发爱因斯坦方程数值解的谱方法

• 批准号: 0554377
• 负责人: Jan Hesthaven
• 金额: $ 66.33万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-01 至 2011-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0554377&HistoricalAwards=false
• 关键词: FRG; Collaborative; Research; Developing; Spectral

In this effort, we form a new interdisciplinary team, comprised ofcomputational mathematicans and astrophysicists, to focus on the development amd analysis of a new generation of simulation tools centered around spectral multi-domain methods. Initial tests have confirmed the potential of such techniqueswhich, however, still require significant algorithmic developments,e.g., efficient nonlinear parallel elliptic solvers, stabilizationtechniques, and novel parallel temporal integration methods, to maturesufficiently. Simultaneously, attention will be paid to problems of anature more specific to the Einstein equations, e.g., the initial dataproblem, control of constraint violating solutions, and suitableboundary conditions.New urgency has been injected into numerical relativity and thedevelopment of computational methods for solving the Einsteinequations by the current deployment of gravitational wave detectors,LIGO and, in the near future, LISA. To fully understand and analyzethe signals measured with such facilities it is essential that a newgeneration of computational tools be available for solving the dynamical Einstein equations over very long times. In this interdiciplinaryeffort we combine expertize in computational mathematics andastrophysics to reach this goal, with the aim of modeling the fulldynamics of a binary pair of black holes, conjectured to be a strongsource of gravity waves as predicted by the general theory of relativity.Thus the effort will not only lead to the development of newcomputational simulation techniniques but also lead to the abilityto test the validity some of the most fundamental physical theoriesknown to mankind.

在这项工作中，我们组建了一个由计算数学家和天体物理学家组成的新的跨学科团队，专注于以光谱多域方法为中心的新一代模拟工具的开发和分析。初步测试已经证实了此类技术的潜力，但仍需要大量的算法开发，例如高效的非线性并行椭圆求解器、稳定技术和新颖的并行时间积分方法，才能充分成熟。 同时，还将关注爱因斯坦方程更具体的性质问题，例如初始数据问题、约束破坏解的控制以及合适的边界条件。数值相对论和求解爱因斯坦方程的计算方法的发展注入了新的紧迫感通过当前部署的引力波探测器 LIGO 以及在不久的将来的 LISA。 为了充分理解和分析用此类设施测量的信号，必须使用新一代计算工具来求解很长一段时间内的动态爱因斯坦方程。在这项跨学科的工作中，我们结合了计算数学和天体物理学的专业知识来实现​​这一目标，目的是对一对双黑洞的完整动力学进行建模，正如广义相对论所预测的那样，双黑洞对被认为是重力波的强大来源。不仅会导致新的计算模拟技术的发展，而且会带来测试人类已知的一些最基本的物理理论的有效性的能力。