Techniques for evolving Einstein's equations

该奖项支持一项研究计划，使用分析和数值技术研究引力波的来源，重点是双黑洞碰撞。LIGO等引力波探测器迫切需要从这些系统的成功数值模拟中获得引力波波形。这些模拟是一个复杂的技术和基础设施的数值解爱因斯坦方程的特殊进步是必要的。该项目包括进一步开发和应用计算物理学和应用数学的最先进技术模拟二元黑洞。爱因斯坦方程的数值解在历史上提出了与爱因斯坦理论固有特征相关的独特问题，例如规范条件和约束违反。作为这个项目的一部分，新的技术，其目标是处理这些独特的问题将被开发或扩展，并应用于双黑洞碰撞。在分析层面，该项目包括开发和应用技术来处理约束不稳定性，爱因斯坦方程的边界条件和坐标条件。在离散层面，它包括多补丁模拟，高阶方法，爱因斯坦方程匹配微扰和其他模块，约束投影和变分积分的方法的开发和应用技术。必要的计算基础设施的发展，以应用这些技术将与仙人掌开发小组在路易斯安那州立大学密切合作。路易斯安那州立大学提供了一个独特的集合专家在数值相对论和科学计算的专业知识可以利用这个项目。

This award supports a research program to use analytical and numerical techniques in the study of sources of gravitational waves with emphasis on binary black hole collisions. Gravitational wave detectors such as LIGO urgently need the gravitational waveforms that would be obtained from the successful numerical simulation of these systems. These simulations are of a complexity such that special advances in techniques and infrastructure for the numerical solution of Einstein's equations are needed. The project includes further development and application to binary black hole simulations of state-of-the-art techniques from computational physics and applied mathematics. The numerical solution of Einstein's equations has historically posed unique, problems associated with features inherent to Einstein's theory, such as gauge conditions and constraint violations. As part of this project novel techniques whose goal is to deal with these unique problems will be developed or extended and applied to binary black hole collisions. At the analytical level the project includes development and application of techniques to deal with constraint instabilities, boundary conditions for Einstein's equations, and coordinate conditions. At the discrete level it includes development and application techniques for multi-patch simulations, high order methods, methods for matching Einstein's equations to perturbative and other modules, constraint projection and variational integrators. The development of the necessary computational infrastructure to apply these techniques will be done in close collaboration with the Cactus development group at LSU. LSU provides an unique assembly of experts in numerical relativity and scientific computing whose expertise can be leveraged by this project.