Collaborative Research: Curvilinear and Multipatch Methods for General Relativistic Astrophysics in the Gravitational Wave Era

最近先进的LIGO对引力波的发现开创了一种新的天文学，一种可能将其发现与电磁和/或中微子观测结果相结合的天文学。多信使天文学通过对同一物体提供截然不同的观点，有望彻底改变我们对宇宙的理解。为了理解这些前所未有的丰富的观测证据，需要进行理论计算，以便将数据与基础物理联系起来。然而，这些都需要新的计算工具来处理越来越广泛的物理治疗、特征尺度和复杂程度。这个项目的主要目的是开发其中的一些工具。该奖项支持的主要目标是为研究强场引力的物理学家和天体物理学家引入两种新技术：多补丁方法和正则化球坐标。前者是一种基础设施，允许对涉及多种物理、多种长度尺度和多种参考框架的异构系统进行有效计算。后者是一种系统地从偏微分方程中去除通常在极轴处产生的奇点的方法。我们期望这两种方法对动态时空中天体物理的研究具有重要的价值。为了进行介绍，我们将推广我们的多补丁基础架构，使其与许多代码自由兼容，包括Athena++，爱因斯坦工具包和Harm3D；我们将在Einstein Toolkit和广泛使用的相对论磁流体力学代码Harm3D的数值相对论和MHD求解中引入正则化球坐标；我们将在选定的科学问题上展示结果。随着先进的LIGO现已全面投入使用，并且即将探测到更多的引力波事件，我们预计，对模拟紧凑双星合并感兴趣的研究人员数量将会激增。我们的新曲线和多补丁框架将大大提高这种模拟的效率和易用性，从而提高对多信使天文学中所有信使——引力波、光子和中微子——所做预测的准确性。

The recent discovery of gravitational waves by Advanced LIGO ushered in a new kind of astronomy, one potentially integrating its findings with those obtained from electromagnetic and/or neutrino observations. Multi-messenger astronomy promises to revolutionize our understanding of the universe by providing dramatically contrasting views of the same objects. To understand this unprecedented wealth of observational evidence, theoretical calculations are required in order to link data with underlying physics. However, these demand the creation of new computational tools that can handle an increasingly wide range of physical treatments, characteristic scales, and levels of complexity. The main thrust of this project is to develop some of these tools.The principal goals supported by this award are to introduce two new techniques into the repertory of physicists and astrophysicists studying strong-field gravity: multipatch methods and regularized spherical coordinates. The former is an infrastructure to permit efficient computation of heterogeneous systems involving multiple kinds of physics, multiple length scales, and multiple reference frames. The latter is a way to systematically remove from partial differential equations the singularity ordinarily arising at the polar axis. We expect both will be of great value to studies of astrophysical objects in dynamical spacetimes. To make this introduction, we will generalize our multipatch infrastructure to make it freely compatible with many codes, including Athena++, The Einstein Toolkit, and Harm3D; we will introduce regularized spherical coordinates into the numerical relativity and MHD solvers of both the Einstein Toolkit and the widely used relativistic magnetohydrodynamics code Harm3D; and we will demonstrate the results on selected science problems. With Advanced LIGO now fully operational and the detection of additional gravitational wave events imminent, we expect that there will be a surge in the number of researchers interested in performing simulations of compact binary mergers. Our new curvilinear and multipatch frameworks will greatly improve the efficiency and ease with which such simulations may be carried out, thereby improving the accuracy of the predictions made for all the messengers---gravitational waves, photons, and neutrinos---of multi-messenger astronomy.