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

Advanced LIGO最近对引力波的发现开创了一种新的天文学，可能将其发现与电磁和/或中微子观测结果相结合。多信使天文学通过提供对同一物体的截然不同的看法，有望彻底改变我们对宇宙的理解。为了理解这一前所未有的观测证据，需要进行理论计算，以便将数据与基础物理联系起来。 然而，这些都需要创建新的计算工具，可以处理越来越广泛的物理治疗，特征尺度和复杂程度。该项目的主要目标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储备库：多面体方法和正则化球坐标。 前者是一个基础设施，允许高效计算的异构系统，涉及多种物理，多种长度尺度，和多个参考系。后者是一种从偏微分方程中系统地去除通常在极轴处产生的奇异性的方法。我们期望这两个方面对研究动态时空中的天体物理学对象具有重要价值。 为了进行介绍，我们将推广我们的多面体基础设施，使其与许多代码免费兼容，包括雅典娜++，爱因斯坦工具包和Harm 3D;我们将在爱因斯坦工具包和广泛使用的相对论磁流体动力学代码Harm 3D的数值相对论和MHD求解器中引入正则化球坐标;我们将展示选定科学问题的结果。随着先进的LIGO现在完全投入使用，以及即将探测到更多的引力波事件，我们预计对模拟紧凑的二元合并感兴趣的研究人员数量将会激增。 我们新的曲线和多面体框架将极大地提高效率和方便，这样的模拟可以进行，从而提高预测的准确性，为所有的信使--引力波，光子和中微子--的多信使天文学。

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.