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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经历了一个重大的转变，由于最近的多项突破-诺贝尔奖获得者发现的引力波从黑洞和中子星星双星系统由美国LIGO探测器，并首次图像的黑洞视界的事件地平线望远镜。引力波是爱因斯坦本人在世纪前预言的，此前从未被直接观测到。正在进行的对来自紧凑双星系统的这些波的观测将用于获得有关宇宙中奇异天体物理物体（如黑洞和中子星）的更多信息。LIGO还产生了重要的衍生技术，并强烈吸引了公众对STEM学科的关注。该项目有助于开发先进的计算模型，这些模型将在LIGO和即将到来的丽莎等太空任务的未来成功中发挥非常关键的作用。该项目的主要目标是开发新的计算技术，以满足LIGO和丽莎数据分析工作的高精度和高效率要求。该项目包括对学生（包括妇女和少数民族）的支持，因此直接有助于学生在重要的STEM领域的指导，培训和保留。学生开发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，包括在国家需求很大的领域。PI之前的研究项目已经在普通媒体上进行了讨论，这项工作也有很大的潜力成功地推广到普通公众。拟议的工作通过开发和调整用于引力波模拟的空间和时间演化方法来解决“宇宙之窗”的挑战。具体来说，目标1将开发一个一维间断Galerkin方法来解决Teukolsky方程。该方法跟踪粒子并将其保持在区域界面处，同时计算Dirac δ函数的导数作为区域边界处的匹配条件。这种方法以极高的精度模拟螺旋相位。然而，一个准确的模拟的暴跌和衰荡阶段，我们需要一个冲击捕获计划，可以处理的狄拉克δ函数的衍生物，并提供高效和准确的多维数值结果。为此，目标2将开发一个非常高阶的韦诺求解器，该求解器将包括处理狄拉克δ函数的三阶导数的能力，并在远离不连续性的区域中变得非常高效。最后，必须根据目标1和2中的空间方案，制定有效和准确的时间演变方法。为此，目标3将为目标1和2中的空间方案制定稳定和有效的时间离散化。对于每个空间离散化，时间离散化方法，如Runge-Kutta和多步Runge-Kutta方法，将被定制，使得该方法是低存储，计算效率高，具有小的分散误差，小的误差常数，和稳定区域，适合于空间离散化，和（对于韦诺）最佳SSP时间步长。在空间和时间离散化的建议的发展将导致更有效的方法，可以准确和有效地处理长时间的积分和狄拉克δ函数及其衍生物的存在。此外，能够在参数空间的相当大的部分上生成波形的准确、高效的数值求解器的开发是引力波计算的重大进步，该奖项反映了NSF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进行评估，被认为值得支持的搜索.