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.

引力波早在世纪就被爱因斯坦预言了。尽管如此，在2015年美国激光干涉引力波天文台（LIGO）探测器获得诺贝尔奖发现黑洞和中子星星双星系统之前，它们从未被直接观测到。这一发现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LIGO未来的成功和即将到来的太空任务（如激光干涉仪太空天线）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射的预期引力波信号，这是过滤噪声数据所必需的。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，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，引起了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经在一般媒体上讨论过，这项工作将继续成功地向公众推广。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，它将开发有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，包括开发一种新的算法，使用不连续Galerkin格式和混合精度二维加权基本无振荡格式。工作还将侧重于开发高阶、正性保持的时间步进方法，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，因为它能够模拟高度逼真的天体物理场景，而这些场景在以前是不可行的，例如两个黑洞在极端质量比极限下快速旋转的系统。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。