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

在这项工作中，我们组建了一个新的跨学科团队，由计算天文学家和天体物理学家组成，专注于围绕光谱多域方法的新一代模拟工具的开发和分析。最初的测试已经证实了这种技术的潜力，然而，仍然需要重大的算法开发，例如，高效的非线性并行椭圆解算器，稳定化技术，以及新颖的并行时间积分方法，以充分成熟。 同时，将注意力放在更具体的爱因斯坦方程，例如，初始数据问题，约束违反解决方案的控制，以及适当的边界条件。新的紧迫性已注入到数值相对论和发展的计算方法，解决爱因斯坦方程的引力波探测器，LIGO和，在不久的将来，丽莎的部署。 为了充分理解和分析用这些设备测量的信号，必须有新一代的计算工具来求解长时间的动力学爱因斯坦方程。在这个跨学科的努力中，我们联合收割机在计算数学和天体物理学方面的专业知识来达到这个目标，目的是模拟一对黑洞的完整动力学，被证明是广义相对论预测的一个强引力波源。因此，这项工作不仅将导致新的计算模拟技术的发展，而且还将导致有能力测试一些最重要的fundamental基本physical物理theories理论known已知to human人类.

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.