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: 0325224
• 负责人: Steven Liebling
• 金额: --
• 依托单位: Long Island University
• 依托单位国家: 美国
• 项目类别: Continuing 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=0325224&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.

这个ITR中等项目将在应用数学，数值相对论，计算机科学和天体物理学方面结合专业知识，以开发模拟现实的强烈野外天体物理系统所需的技术。为此，选择了一个驱动程序问题，涉及求解爱因斯坦的一般相对论理论的方程，该理论与电磁和流体动力学结合，以描述诸如黑洞形成和黑洞周围物质的积聚等现象。从历史上看，这种努力遇到了许多困难，因此将在这些问题上带来许多先进的技术。将使用双曲线方程的属性来研究这种发展中的稳定性，并开发数值技术以利用有用的分析属性。同时，分布式自适应网格改进的开发将允许最有效地利用计算能力。通过这些和相似方程式建模了广泛的物理现象，因此这里研究的技术和发展应适用于广泛的问题。 研究的身体情况引起了很多兴趣，更好的动态模型将尤其是Ligo项目中涉及的分析以检测引力波。该项目还将在这些方法中培训科学家，并通过论文和会议来宣传它们。