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

高级LIGO最近发现的引力波开启了一种新的天文学，一种可能将其发现与电磁和/或中微子观测获得的结果相结合的天文学。多信使天文学通过提供对相同物体的截然不同的观点，有望彻底改变我们对宇宙的理解。为了理解这一史无前例的丰富的观测证据，需要进行理论计算，以便将数据与潜在的物理联系起来。然而，这些都需要创造新的计算工具，能够处理越来越广泛的物理治疗、特征规模和复杂程度。这个项目的主旨是开发其中的一些工具。该奖项支持的主要目标是将两种新技术引入物理学家和天体物理学家研究强场引力的库中：多面体方法和正则化球坐标法。前者是一种基础设施，允许对涉及多种物理、多个长度尺度和多个参照系的异类系统进行有效计算。后者是一种从偏微分方程组中系统地去除通常在极轴上出现的奇异性的方法。我们希望这两种方法对研究动力学时空中的天体物理对象有很大的价值。为了进行介绍，我们将推广我们的多面体基础设施，使其与许多程序自由兼容，包括雅典娜、爱因斯坦工具包和Harm3D；我们将在爱因斯坦工具包和广泛使用的相对论磁流体力学程序Harm3D的数值相对论和MHD解算器中引入正则化的球坐标；我们将在选定的科学问题上演示结果。随着Advanced LIGO现在完全投入使用，以及即将探测到更多的引力波事件，我们预计将有更多的研究人员对模拟紧凑的双星合并感兴趣。我们新的曲线和多面体框架将极大地提高进行此类模拟的效率和简便性，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-的预测的准确性。

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.