Numerical Relativity Simulations with the New Mesh Code

该奖项支持相对论和相对论天体物理学的研究，并解决了NSF“宇宙之窗”大构想的优先领域。美国国家科学基金会的LIGO探测器首次直接探测到合并黑洞发出的引力波，这是引力物理学的历史性突破，并获得了2017年的诺贝尔物理学奖。同样令人震惊的是引力波和电磁波谱上的信号，从伽马射线到无线电波，从两颗中子星的吸入和合并。有了这些以及随后许多类似的探测，我们打开了一扇通往宇宙的新窗口。预计还会有更多来自其他天体物理来源的探测。该项目旨在通过对控制这些非常密集和奇异物体的基本方程进行数值模拟，对黑洞和中子星等致密物体进行预测。为此，一种名为Nmesh的新计算机程序正在开发中。Nmesh将在目前由数百万个计算核心组成的大型超级计算机上运行。为了充分有效地利用如此多的核，需要各种先进的编程技术来并行运行Nmesh。虽然这个项目的主要和直接的科学目标是模拟黑洞和中子星，但Nmesh也可以用来模拟其他类型的方程。一旦经过良好的测试，Nmesh就会向公众开放。这将直接使数值相对论领域的其他研究人员受益，但由于Nmesh非常通用，它也应该使其他需要解决由不同方程控制的不同问题的研究人员受益。部分研究将与德国耶拿大学的相对论小组密切合作进行。两所院校的教师和学生都计划参观。这次交换将对来自佛罗里达大西洋大学和耶拿大学的学生都有教育上的好处。这个项目主要关注由黑洞或中子星组成的双星。当两个物体靠近时，需要对爱因斯坦方程进行完全非线性的数值模拟，以预测启发和随后合并的最后部分。该项目旨在通过进行数值模拟来详细了解这种紧密天体的双吸气和合并。使用Nmesh程序，它将提供引力波形目录，以及涉及物质的抛射信息。因此，为了获得更高的精度结果，计划进一步开发和升级Nmesh。这将使高质量比黑洞吸进的研究以及双中子星模拟的精度得到提高。研究结果还将用于改进和校准分析波形模型，以预测引力波，而无需进行昂贵的数值模拟。Nmesh的升级不仅包括先进的并行化方法，还将包括在不连续Galerkin方法框架内处理冲击的方法的开发。后一种方法在数值相对论中仍然是新的，因此需要特别注意。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。

This award supports research in relativity and relativistic astrophysics and it addresses the priority areas of NSF's "Windows on the Universe" Big Idea. The first direct detection of gravitational waves emitted from merging black holes, by the NSF's LIGO detectors, was a historic breakthrough in gravitational physics, and led to the Noble prize in physics in 2017. Equally stunning was the detection of both gravitational waves and signal across the electromagnetic spectrum from gamma rays to radio waves, from the inspiral and merger of two neutron stars. With these and numerous subsequent similar detections a new window to the universe has been opened. More detections from a variety of other astrophysical sources are also anticipated. This project aims at making predictions about compact objects such as black holes and neutron stars, by running numerical simulations of the basic equations that govern such very dense and exotic objects. For this purpose a new computer program called Nmesh is being developed. Nmesh will be run on large scale supercomputers that nowadays consist of millions of compute cores. Making full and efficient use of so many cores involves various advanced programming techniques to run Nmesh in parallel. While the primary and immediate scientific goal of this project is the simulation of black holes and neutron stars, Nmesh can also be used to simulate other types of equations. Once it is well tested, Nmesh will be made publicly available. This will directly benefit other researchers in the area of numerical relativity, but since Nmesh is quite general it should also benefit others that need to solve different problems that are governed by different equations. Part of the research will be carried out in close collaboration with the relativity group at the University of Jena in Germany. Visits by faculty and students from both institutions are planned. This exchange will have educational benefits for students from both Florida Atlantic University (FAU) and the University of Jena.This project mainly focuses on binaries made up of black holes or neutron stars. When the two objects get close, fully non-linear numerical simulations of the Einstein equations are required to make predictions about the final part of the inspiral and subsequent merger. The project is aimed at gaining a detailed understanding of such compact-object binary inspirals and mergers by performing numerical simulations. Using the Nmesh program it will provide gravitational waveform catalogs, as well as information about ejecta when matter is involved. To achieve high accuracy results it is thus planned to further develop and upgrade Nmesh. This will enable the study of high mass ratio black hole inspirals, as well as binary neutron star simulations with improved accuracy. The results will also be used to improve and calibrate analytical waveform models to predict gravitational waves without needing to perform expensive numerical simulations. The upgrades to Nmesh will not only include advanced parallelization methods, but will also include the development of methods to treat shocks, within the framework of discontinuous Galerkin methods. The latter method is still new in numerical relativity, and thus requires special attention.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.