High Order Numerical Methods for Gravitational Wave Computations

引力波计算的高阶数值方法

基本信息

批准号：
1912716
负责人：
Scott Field
金额：
$ 27.5万
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：
2019
资助国家：
美国
起止时间：
2019-07-01 至 2023-09-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1912716&HistoricalAwards=false
关键词：
Order Numerical Methods Gravitational Wave

项目摘要

The research area of black hole astrophysics has experienced a major transformation as a result of multiple recent breakthroughs -- a Nobel Prize-winning discovery of gravitational waves from black hole and neutron star binary systems by the US LIGO detectors, and the first-ever image of the horizon of a black hole by the Event Horizon Telescope. Gravitational waves were predicted by Einstein himself a century ago and had never been directly observed before. Ongoing observations of these waves from compact binary systems will be used to obtain additional information about exotic astrophysical objects in the universe like black holes and neutron stars. LIGO has also generated significant spin-off technologies and strongly drawn public attention towards STEM disciplines. This proposed project aids in the development of advanced computational models that will play a very critical role in the future success of LIGO and upcoming space-borne missions like LISA. The main objective of the proposed project is to develop new computational techniques to meet the high-accuracy and high-efficiency requirements set by the LIGO and LISA data-analysis effort. This project includes support for students (including women and minorities) and therefore directly contributes to student mentorship, traineeship, and retention in an important STEM area. The computational skills that the students develop are broadly applicable, and therefore would allow them access to a variety of career options, including in areas of great national need. Previous research projects by the PIs have been discussed in the general media, and this work also has great potential at being successful for outreach to the general public.The proposed work addresses the "Windows on the Universe" challenge by developing and adapting spatial and time-evolution methods for use in gravitational wave simulations. Specifically, Aim 1 will develop a one dimensional discontinuous Galerkin method to solve the Teukolsky equations. This method tracks the particle and keeps it at the domain interfaces while computing the derivatives of the Dirac delta functions as matching conditions at the boundary of the domain. This approach simulates the in-spiral phase to extremely high accuracy. However, for an accurate simulation of the plunge and ring-down phase we require a shock capturing scheme that can handle derivatives of the Dirac delta function and provide highly efficient and accurate multi-dimensional numerical results. For this, Aim 2 will develop a very high order WENO solver that will include the ability to handle up to third derivatives of the Dirac delta function and be made highly efficient in the regions away from the discontinuity. Finally, efficient and accurate time evolution approaches must be tailored to the spatial schemes in Aims 1 and 2. For this, Aim 3 will develop stable and efficient time-discretizations tailored for the spatial schemes in Aims 1 and 2. For each spatial discretization, time-discretization approaches such as Runge-Kutta and multi-step Runge-Kutta methods will be tailored such that the methods are low storage, computationally efficient, have small dispersion errors, small error constants, and stability regions that are tailored to the spatial discretization, and (for WENO) optimal SSP time-steps. The proposed developments in both spatial and temporal discretizations will lead to more efficient methods that can accurately and efficiently handle long time-integration and the presence of Dirac delta functions and its derivatives. Furthermore, the development of an accurate, efficient numerical solver capable of generating waveforms over sizable portions of the parameter space is a major advance in the computation of gravitational waves, and will thus have a major impact on the field of gravitational wave science.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.

黑洞天体物理学的研究领域由于最近的多次突破而经历了重大的转变 - 美国Ligo探测器从Black Hole和Neutron Star Binary Systems赢得了诺贝尔奖的重力波，以及有史以来第一个图像事件地平线望远镜的黑洞的地平线。爱因斯坦本人在一个世纪前预测了引力波，以前从未直接观察过。从紧凑型二元系统中对这些波的持续观察将用于获取有关宇宙中外来天体物理物体（如黑洞和中子星）的其他信息。 Ligo还产生了大量的衍生技术，并引起了公众对STEM学科的关注。这项拟议的项目有助于开发先进的计算模型，这些模型将在LIGO和即将到来的太空传播任务（如Lisa）的未来成功中发挥至关重要的作用。拟议项目的主要目的是开发新的计算技术，以满足LIGO和LISA数据分析工作设定的高准确性和高效率要求。该项目包括对学生（包括妇女和少数族裔）的支持，因此直接为学生指导，实习生和在重要的STEM领域的保留做出贡献。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，包括在国家需求巨大的领域。 PIS的先前研究项目已经在通用媒体上进行了讨论，这项工作也有很大的潜力，可以成功地向公众推广。拟议的工作通过开发和调整空间和时间来应对“宇宙中的Windows”挑战 - 用于引力波模拟的进化方法。具体而言，AIM 1将开发一种一维不连续的Galerkin方法来解决Teukolsky方程。该方法跟踪粒子并将其保持在域界面，同时计算Dirac Delta的衍生物作为域边界处的匹配条件。这种方法模拟了刺激阶段的精度极高。但是，为了准确模拟暴跌和降落相，我们需要一个可以处理Dirac Delta函数的衍生物并提供高效，准确的多维数值结果的冲击捕获方案。为此，AIM 2将开发出非常高的WENO求解器，其中包括处理多达Dirac Delta功能的第三个衍生品的能力，并在远离不连续性的地区高效。最后，必须针对目标1和2中的空间方案量身定制有效，准确的时间演变方法。为此，AIM 3将在AIMS 1和2中为空间方案量身定制的稳定且有效的时间消除量。对于每个空间离散，每个空间离散，时间消化方法，例如runge-kutta和多步runge-kutta方法，将量身定制，以使该方法的存储时间低，计算上有效，分散错误，小误差常数，较小的误差常数和稳定性区域，这些稳定性和稳定性区域量身定制为空间隔离和（对于WENO）最佳的SSP时间步长。空间和时间离散化的拟议发展将导致更有效的方法，这些方法可以准确有效地处理长时间整合，并存在Dirac Delta函数及其衍生物。此外，开发能够在参数空间的相当大部分上产生波形的精确，有效的数值求解器是重力波的计算中的重大进步，因此将对引力波科学领域产生重大影响。反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响审查标准来评估值得支持。