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

开发高阶稳定且有效的方法来长时间模拟引力波形

• 批准号: 2309609
• 负责人: Scott Field
• 金额: $ 34.91万
• 依托单位: University of Massachusetts, Dartmouth
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-07-15 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2309609&HistoricalAwards=false
• 关键词: Developing; Order; Stable; Efficient; Methods

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.

一个世纪前爱因斯坦预测了引力波。尽管如此，在2015年，基于美国的激光干涉仪重力波动仪（LIGO）检测器对诺贝尔奖获得黑洞和中性恒星二元系统的发现之前，他们从未直接观察到它们。这种检测预示着预示着在迫切需要的迫切需要的迫切需要的模型，这将导致迫在眉睫的迫在眉睫的模型，从而导致了迫切需要的关键范围，这是迫切需要的，这是迫切需要的。像激光干涉仪空间天线。需要高临界力引力波模拟，以产生从这些系统中发出的预期重力波信号，超过数十万个轨道循环，这些轨道循环需要过滤噪声数据。该项目的主要目的是开发新的计算技术，以准确有效地模拟引力波，它们将使科学家能够最大程度地提高当前和未来探测器的科学输出。这些努力为宇宙打开了一个窗口，并吸引了公众的兴趣以及年轻一代的科学家。研究人员先前的研究项目已经在通用媒体上进行了讨论，这项工作将继续与公众宣传。学生发展的计算技能广泛适用，因此，将使他们获得各种职业选择，包括在紧急国家需求的领域中。该项目旨在开发先进的数学和计算模型，以准确模拟大型质量二进制二进制黑洞系统，这对于检测引力波是至关重要的。特别是，它将开发出高效稳定的高阶方法，可以处理S =±2 Teukolsky模型的高度单数源术语，包括使用不连续的Galerkin方案开发新算法和混合精度2D加权的混合精度基本上是非激发方案。工作还将着重于开发具有最小化相位和分散误差的高阶，积极的时间步变方法，以提高模拟的准确性。研究结果将通过实现以前不可行的高度现实的天体物理场景的建模来重大影响引力波发现的领域，例如两个黑洞都在极端质量比率上迅速旋转的系统。该奖项反映了NSF的法定任务，反映了通过评估基金会和广泛的影响和广泛的支持和广泛的支持。