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

协作 ITR：分布式自适应网格细化计算问题的严格技术

• 批准号: 0326311
• 负责人: Luis Lehner
• 金额: --
• 依托单位: Louisiana State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-09-01 至 2009-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0326311&HistoricalAwards=false
• 关键词: Collaborative; ITR; Rigorous; Techniques; Computational

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.

该 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，涉及求解与电磁学和流体动力学耦合的爱因斯坦广义相对论方程，以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许多困难，因此将采用许多先进技术来解决这些问题。将使用双曲方程的性质来研究在这种演化中保持稳定性，并且将开发数值技术以利用有用的分析性质。同时，分布式自适应网格细化的发展将允许最有效地利用计算能力。这些和类似的方程可以对广泛的物理现象进行建模，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引起了人们的极大兴趣，更好的动力学模型将有益于 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，并通过论文和会议进行宣传。