Spectral Elements for Numerical Relativity andGravitational Wave Source Modeling

2015年首次直接探测到引力波，是引力物理学的历史性突破。第一次观测与两个黑洞的碰撞有关，而在2017年8月，首次观测到了来自两颗中子星合并的引力波。中子星合并在多信使天文学中引起了极大的兴趣，因为它们还伴随着大范围的电磁辐射。对这些观测结果的解释需要理论模型，但二元合并的建模仍然是一个重大挑战。该提案的重点是为数值广义相对论开发新的数值方法，但与为引力波源提供模型的持续努力有很强的联系。在求解偏微分方程组的各种高阶方法中，一种特殊的谱元素方法--间断Galerkin方法是近年来出现的一种成功的通用方法。为了实现数值广义相对论的下一代计算机模拟，目标是开发和实现广义相对论、广义相对论流体力学和磁流体动力学的间断Galerkin方法。仍然存在重大挑战，包括为几何学和一般相对论流体力学，特别是对于激波的处理，寻找最优的间断Galerkin公式。为了提高效率，目标是实现并行自适应网格加密，包括空间和时间上的加密。然而，这种技术中的大部分还不能用于数值相对论，所以计划推动新的计算基础设施的发展。数值相对论的主要挑战是，我们是在实现一个移动的目标(新的方程、新的数值方法、新的硬件)，因此我们需要专业的软件工程、协作基础设施以及与我们的科学推动者的密切联系。其目标是超越简单的测试案例，通过对引力波源建模的全功能模拟来推动数值相对论不连续Galerkin方法的发展。首要目标是为双星中子星和引力波的物理学提供一个理论框架。

The first direct detection of gravitational waves in 2015 was a historic breakthrough in gravitational physics. The first observations were associated with the collision of two black holes, while in August 2017 gravitational waves from the merger of two neutron stars were observed for the first time. Neutron star mergers are of great interest in multi-messenger astronomy since they are also accompanied by a wide range of electromagnetic radiation. The interpretation of these observations requires theoretical models, but modeling of binary mergers remains a major challenge.The focus of the proposal is on the development of new numerical methods for numerical general relativity, but with strong ties to the ongoing efforts to provide models for gravitational wave sources. Among the different high-order methods to solve partial differential equations, a particular spectral element method, the discontinuous Galerkin method, has emerged in recent years as a successful general purpose paradigm. To enable the next generation of computer simulations in numerical general relativity, the goal is to develop and implement discontinuous Galerkin methods for general relativity, general relativistic hydrodynamics and magneto hydrodynamics. There are major challenges still ahead, including finding optimal discontinuous Galerkin formulations for the geometry and for general relativistic hydrodynamics, in particular for the treatment of shocks. For high efficiency, the goal is to implement the method with parallel adaptive mesh refinement, involving refinements in space and time.Most of this technology, however, is not available yet for numerical relativity, so the plan is to push the development of a new computational infrastructure. The main challenge in numerical relativity is that we are implementing for a moving target (new equations, new numerical methods, new hardware), so we require professional software engineering, a collaborative infrastructure, and close contact to our science drivers. The goal is to move beyond simple test cases and drive the development of the discontinuous Galerkin method for numerical relativity by full-featured simulations for gravitational wave source modeling. The overarching goal is to provide a theoretical framework for the physics of binary neutron stars and gravitational waves.