Techniques for evolving Einstein's equations

该奖项支持一个研究项目，利用分析和数值技术研究引力波的来源，重点是双黑洞碰撞。像LIGO这样的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的引力波波形。这些模拟非常复杂，因此需要在技术和基础设施方面取得特殊进展，以便对爱因斯坦方程进行数值求解。该项目包括进一步开发和应用计算物理和应用数学中最先进的技术来模拟双黑洞。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。作为该项目的一部分，旨在解决这些独特问题的新技术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，它包括多补丁模拟的开发和应用技术，高阶方法，将爱因斯坦方程与微扰和其他模块匹配的方法，约束投影和变分积分器。应用这些技术的必要计算基础设施的开发将与LSU的Cactus开发小组密切合作完成。路易斯安那州立大学在数值相对论和科学计算方面提供了一个独特的专家组合，他们的专业知识可以被这个项目所利用。

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.