Boosting Algorithmic Efficiency: Numerical Relativity in Dynamical, Curvilinear Coordinates

爱因斯坦的广义相对论(GR)提供了目前科学上对引力的最好理解。它预测了黑洞和中子星等奇异物体的存在，以及被称为引力波的时空涟漪的存在。这些预测推动了激光干涉仪引力波天文台(LIGO)的建设，到目前为止，LIGO已经探测到了几个来自碰撞黑洞的引力波信号和一个来自碰撞中子星的信号。由于他们为实现这些探测所做的努力，LIGO的领导人被授予2017年诺贝尔物理学奖。为了更深入地了解是什么产生了观测到的引力波，LIGO数据分析将观测到的引力波与爱因斯坦的GR理论在大量可能的情况下预测的引力波进行了比较。构建可靠的理论模型需要数值相对论领域提供的GR基本方程的完整解。该项目建立在该领域最新进展的基础上，以开发新的软件，极大地降低生成这些解决方案的成本(在内存中)。在数值相对论在很大程度上依赖超级计算机之前，这个新软件将使即使是消费级台式计算机也能够生成LIGO数据分析所需的合并黑洞的理论预测。在资助期的后半部分，该软件将具备超级计算机的能力，能够以最先进的精度在超级计算机上模拟合并中子星(需要更多的内存)。通过解锁消费级台式机作为数字相对论的强大工具，该项目具有使公众以前所未有的方式参与科学的潜力。这将通过将该软件整合到SETI@Home的“BOINC”志愿者计算基础设施中来实现。希望当LIGO探测到一对正在合并的黑洞时，将启动数千次黑洞合并计算，以造福于LIGO科学，每一次计算都在一台运行我们的黑洞@Home软件的消费级台式计算机上进行。为了教育公众并在当地和全球范围内宣传这一志愿者计算项目，西弗吉尼亚大学团队将在附近的高中举行会议，并为广泛收集的新闻网站“The Conversation”撰写文章。数值相对论(NR)在计算机上完整地解决了爱因斯坦的广义相对论方程(GR)。对NR码的算法和数学基础的改进最近在该领域的成熟中达到顶峰，使其超越了原则证明计算，进入了预测天体物理学的领域。在过去的两年里，基于NR的引力波(GW)理论预测是揭示LIGO最近GW发现中的二元参数的核心。既然多信使天体物理学的时代已经到来，涉及引力场和磁化流体动力学的物理场景将需要在长度和时间尺度上跨越数量级进行建模。NR代码通过动态调整其空间数值网格以更好地对空间进行采样来桥接这些尺度，但当前的算法不考虑这些系统中的近对称性或依赖于复杂的网格算法。拟议的项目涉及开发一种新的NR代码，其独特目标是既算法简单又高效，在最大化科学影响的同时最大限度地减少计算和人力投入。我们称其为SENR，简单、高效的NR码。SEIR的独特之处在于，它的目标是在一个单一的、动态的、类似双球面的空间网格上对紧凑的双星进行NR模拟。利用底层系统中的近对称性可以比最广泛采用的NR方法减少数量级的计算量，最小化网格管理基础设施大大简化了数值误差的解释和新物理模块的添加。Senr在NR中建立了一种新的、高度健壮的方法，用于在具有坐标奇异性的静态曲线空间网格(例如球极坐标)上求解带有流体动力学的GR场方程，PI的团队正在将该方法扩展到任意的动态坐标系。为该项目开发的基于Python的代码生成工具NRPy+加速了Senr的开发。遵循软件设计的最佳实践，小的Senr代码库在添加了每个主要功能后进行了仔细的优化，以最大限度地发挥科学影响。Senr的内存效率开启了桌面作为NR工具的大门，使我们能够启动第一个主要的志愿者计算工作，为双黑洞生成一个巨大的基于NR的GW目录。此外，SENR的可扩展性将使我们能够利用超级计算资源来生成非常大的双中子星GW星表。基础设施的简单性大大减少了添加新物理模块所需的工作，我们计划将基于蒙特卡洛的光子和中微子反馈纳入我们的紧凑型二元模拟中，以实现最先进的真实感。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Einstein's theory of general relativity (GR) provides science's current best understanding of gravity. It predicts the existence of bizarre objects like black holes and neutron stars, and ripples in spacetime called gravitational waves. These predictions motivated the construction of the Laser Interferometer Gravitational-wave Observatory (LIGO), which has detected several gravitational wave signals from colliding black holes and one signal from colliding neutron stars so far. For their efforts in making these detections possible, the leaders of LIGO were awarded the 2017 Nobel Prize in Physics. To obtain a deeper understanding about what produced the observed gravitational waves, LIGO data analysis compares observed waves with those predicted by Einstein's theory of GR for a very large number of possible scenarios. Construction of reliable theoretical models requires the full solutions to the equations underlying GR, provided by the field of numerical relativity. This project builds upon recent advances in this field to develop new software that greatly reduces the cost (in memory) of generating these solutions. Where before numerical relativity largely depended upon supercomputers, this new software will enable even consumer-grade desktop computers to generate needed theoretical predictions of merging black holes needed for LIGO data analysis. In the latter half of the funding period, the software will be made supercomputer-capable to enable (the far more memory-hungry) simulations of merging neutron stars on supercomputers with state-of-the-art accuracy. By unlocking the consumer-grade desktop as a powerful tool for numerical relativity, this project has the potential to enable the public to participate in the science in unprecedented ways. This will be made possible by incorporating this software into SETI@Home's "BOINC" volunteer computing infrastructure. The hope is that when LIGO detects a pair of merging black holes, thousands of black hole merger calculations will be launched for the benefit of LIGO science, each on a consumer-grade desktop computer running our "BlackHoles@Home" software. To educate the public and advertise this volunteer computing project both locally and globally, the West Virginia University group will give convocations in nearby high schools and write articles for the widely aggregated news site "The Conversation".Numerical relativity (NR) solves Einstein's equations of general relativity (GR), in full, on the computer. Improvements to the algorithmic and mathematical underpinnings of NR codes have recently culminated in a coming-of-age for the field, moving it beyond proof-of-principle calculations and into the realm of predictive astrophysics. Over the past two years, NR-based theoretical predictions of gravitational waves (GWs) were central to uncovering the binary parameters in LIGO's recent GW discoveries. Now that the age of multi-messenger astrophysics has arrived, physical scenarios involving gravitational field and magnetized fluid dynamics spanning orders of magnitude in length scale and timescale will need to be modeled. NR codes bridge these scales by dynamically adjusting their spatial numerical grids to better sample the space, but current algorithms do not account for near-symmetries in these systems or rely on complex mesh algorithms. The proposed project involves the development of a new NR code with the unique goal of being both algorithmically simple and highly efficient, minimizing computational and human effort while maximizing scientific impact. We call it SENR, the Simple, Efficient NR code. SENR is unique in its aim to perform NR simulations of compact binary inspirals atop a single, dynamical, bispherical-like spatial grid. Exploiting near-symmetries in the underlying system can reduce computational cost over the most widely-adopted NR methods by orders of magnitude, and minimizing the grid management infrastructure greatly simplifies the interpretation of numerical errors and the addition of new physics modules. SENR builds on a new, highly-robust approach in NR for solving the GR field equations with hydrodynamics on static curvilinear spatial grids with coordinate singularities (e.g., spherical polar coordinates), and the PI's team is extending the approach to arbitrary, dynamical coordinate systems. Development of SENR is accelerated by a Python-based code-generation tool developed for this project called NRPy+. Following best-practices in software design, the small SENR codebase is carefully optimized after each major feature is added to maximize scientific impact. SENR's memory efficiency unlocks the desktop as a tool for NR, enabling us to launch the first major volunteer computing effort to generate an enormous NR-based GW catalog for binary black holes. Further, SENR's scalability will enable us to leverage supercomputing resources to generate a very large double neutron star GW catalog as well. Simplicity in infrastructure greatly reduces effort required to add new physics modules, and we plan to incorporate Monte-Carlo-based photon and neutrino feedback to enable state-of-the-art realism in our compact binary simulations.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.