Developing High Order Stable and Efficient Methods for Long Time Simulations of Gravitational Waveforms

爱因斯坦在一个世纪前就预言了引力波。尽管如此，在2015年美国激光干涉仪引力波天文台（LIGO）探测器发现黑洞和中子星双星系统获得诺贝尔奖之前，它们从未被直接观测到。这一探测预示着引力波天体物理学领域的重大科学变革，这导致了对先进计算模型的迫切需求，这些模型将在未来LIGO和即将到来的空间任务（如激光干涉仪空间天线）的成功中发挥关键作用。需要高精度的引力波模拟来产生这些系统在数十万个轨道周期内发出的预期引力波信号，这需要过滤噪声数据。该项目的主要目标是开发新的计算技术，以准确有效地模拟引力波，这将使科学家能够最大限度地提高当前和未来探测器的科学产出。这些努力打开了一扇通往宇宙的窗户，吸引了普通公众和年轻一代科学家的兴趣。调查人员以前的研究项目已在一般媒体上进行了讨论，这项工作将继续成功地向公众推广。学生们所培养的计算技能是广泛适用的，因此，将使他们能够获得各种职业选择，包括在国家迫切需要的领域。该项目旨在开发先进的数学和计算模型，以精确模拟大质量比双黑洞系统，这对探测引力波至关重要。特别是，它将开发高效和稳定的高阶方法，可以处理s =±2 Teukolsky模型的高度奇异源项，包括使用不连续Galerkin格式和混合精度二维加权基本非振荡格式的新算法的开发。工作还将侧重于开发高阶，保持正数的时间步进方法，使相位和色散误差最小化，以提高模拟的准确性。该研究成果将对引力波发现领域产生重大影响，因为它使以前不可能实现的高度真实的天体物理场景（例如两个黑洞在极端质量比极限下快速旋转的系统）的建模成为可能。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Gravitational waves were predicted by Einstein a century ago. Still, they had never been directly observed before the Nobel Prize-winning discovery of black hole and neutron star binary systems by the US-based Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors in 2015. This detection heralded a major scientific transformation in the gravitational wave astrophysics field, which led to an urgent need for advanced computational models that will play a critical role in the future success of LIGO and upcoming space-borne missions like Laser Interferometer Space Antenna. High-accuracy gravitational wave simulations are needed to produce the expected gravitational wave signal emitted from these systems over hundreds of thousands of orbital cycles, which are required to filter noisy data. The main objective of this project is to develop new computational techniques to accurately and efficiently simulate gravitational waves that will allow scientists to maximize the scientific output of current and future detectors. These efforts open a window into the universe and capture the interest of the general public as well as a younger generation of scientists. Previous research projects by the investigators have been discussed in the general media, and this work will continue to be successful in outreach to the general public. The computational skills that the students develop are broadly applicable and, therefore, would allow them access to various career options, including in areas of urgent national need.The project aims to develop advanced mathematical and computational models to accurately simulate large-mass-ratio binary black hole systems, which are crucial for detecting gravitational waves. In particular, it will develop efficient and stable high-order methods that can handle the highly singular source terms of the s = ±2 Teukolsky model, including the development of a novel algorithm using a discontinuous Galerkin scheme and a mixed precision 2D weighted essentially non-oscillatory scheme. Work will also focus on developing high-order, positivity-preserving time-stepping methods with minimized phase and dispersion errors to enhance the accuracy of the simulations. The research outcomes will significantly impact the field of gravitational wave discoveries by enabling the modeling of highly realistic astrophysical scenarios that were previously infeasible, such as systems in which both black holes are rapidly spinning in the extreme mass ratio limit.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.