Compact Object Studies in Computational Relativistic Astrophysics via Discontinuous Galerkin Finite Element Methods

计算相对论天体物理学领域已经到达了对许多观测到的和预期的辐射源进行预测建模的边缘。随着社区努力提高所采用的物理模型的真实性，进展受到大规模使用计算方法的复杂性和困难的严重阻碍。随着硬件架构的发展，许多以前高效的算法只能利用新硬件的一小部分功能，需要开发和改进新的算法。 现代数值方法，如不连续伽辽金有限元（DGFE）在过去十年中在其他领域取得了很大的成功，但尚未设法取得进展，计算相对论天体物理学。 我将研究适合爱因斯坦和广义相对论磁流体力学方程的DGFE方法，设计适合现代硬件架构的相应有效实现，并将其作为我的开源软件基础设施的一部分。我将利用这些来研究天体物理系统，特别是黑洞双星和核心坍缩超新星，提高精度和/或减少模拟等待时间至少一个数量级。这反过来又将允许将新的物理学纳入这些系统的研究中，这在今天是遥不可及的。

The field of Computational Relativistic Astrophysics has arrived at the verge of predictive modeling of many observed and expected sources of radiation. As the community strives to increase the realism in the employed physics models, progress is severely hindered by the complexity and difficulties in using computational methods at large scales. As hardware architectures evolve, many formerly highly efficient algorithms can exploit only a fraction of the power of newer hardware, and novel algorithms need to be developed and refined. Modern numerical methods, such as Discontinuous Galerkin Finite Elements (DGFE) have enjoyed much success in the past decade in other fields, but have not yet managed to make an inroad to Computational Relativistic Astrophysics. I will research DGFE methods suitable for the Einstein and General Relativistic Magneto-Hydrodynamics equations, design respective efficient implementations suitable for modern hardware architectures, and make these available as part of my open-source software infrastructure. I will employ these to study astrophysical systems, in particular black hole binaries and core-collapse supernovae, increasing accuracy and/or reducing simulation waiting times by at least an order of magnitude. This will in turn allow incorporating new physics into the study of these systems that is far out of reach today.