Collaborative ITR: Rigorous Techniques in Computational Problems with Distributed Adaptive Mesh Refinement

这个ITR-Medium项目将结合联合收割机在应用数学、数值相对论、计算机科学和天体物理学方面的专业知识，开发模拟现实强引力场天体物理系统所需的技术。为此，选择了一个驱动问题，该问题涉及求解爱因斯坦广义相对论的方程，耦合到电磁学和流体力学来描述黑洞形成和黑洞周围物质吸积等现象。这些努力在历史上遇到了一些困难，因此，一些先进的技术将被带到承担这些problems.Maintaining稳定性，在这样的演变将研究使用双曲方程的属性，和数值技术将被开发，以利用有用的分析性能。与此同时，分布式自适应网格加密技术的发展将使计算能力得到最有效的利用。这些方程和类似的方程可以模拟各种物理现象，因此本文所研究的技术和发展应该适用于各种问题。 研究中的物理情况引起了人们的极大兴趣，更好的动力学模型将特别有益于LIGO项目中探测引力波的分析。该项目还将对科学家进行这些方法的培训，并通过论文和会议宣传这些方法。

This ITR-Medium project will combine expertise in applied mathematics, numerical relativity, computer science, and astrophysics to develop techniques needed to simulate realistic strong-gravitational-field astrophysical systems. To this end, a driver-problem is chosen that involves solving the equations of Einstein's theory of general relativity coupled to electromagnetism and hydrodynamics to describe phenomena such as black hole formation and the accretion of matter around a black hole. Such efforts have historically encountered a number of difficulties, and therefore a number of advanced techniques will be brought to bear upon these problems.Maintaining stability in such evolutions will be studied using properties of hyperbolic equations, and numerical techniques will be developed to take advantage of useful analytical properties. At the same time, development of distributed adaptive mesh refinement will allow for the most efficient use of computational power.A wide range of physical phenomena are modeled by these and similar equations, and thus the techniques and developments studied here should be applicable to a wide range of problems. The physical situations under study attract much interest, and better models of their dynamics willbenefit, in particular, the analysis involved in the LIGO project to detect gravitational waves. This project also will train scientists in these methods as well as publicize them with papers and conferences.