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

这个ITR-Medium项目将结合应用数学、数值相对论、计算机科学和天体物理方面的专业知识，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，该问题涉及求解与电磁学和流体力学相耦合的爱因斯坦广义相对论方程，以描述诸如黑洞形成和黑洞周围物质吸积等现象。这种努力在历史上遇到了许多困难，因此将使用一些先进的技术来解决这些问题。将利用双曲型方程的性质来研究在这种演变过程中保持稳定性，并将开发数值技术来利用有用的分析性质。同时，分布式自适应网格加密的发展将使计算能力得到最有效的利用。许多物理现象都是由这些方程和类似的方程模拟的，因此这里研究的技术和发展应该适用于广泛的问题。正在研究的物理情况吸引了很多人的兴趣，更好的动力学模型将有助于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.