Efficient Numerical Methods For Material Transport On Moving Interfaces And Hamilton Jacobi Equations

移动界面上物质传输的有效数值方法和哈密顿雅可比方程

• 批准号: 0513073
• 负责人: Hong-Kai Zhao
• 金额: $ 18万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-15 至 2009-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0513073&HistoricalAwards=false
• 关键词: Efficient; Numerical; Methods; Material; Transport

The objective of this proposed project is to develop efficient computational algorithms for two important classes of problems. The first is to develop efficient numerical methods for material transport on moving interfaces with global dynamics. The main difficulty is the coupling of the global dynamics, the moving interface and the material distribution on the interface. The investigator will develop efficient and robust methods that can(1) track material transport on moving interfaces,(2) couple interfacial dynamics with global dynamics.In particular the developed numerical methods will be used to study the effect of surfactants in two phase flow. The second is to analyze and extend the fast sweeping method, which is an efficient iterative method recently developed for Eikonal equations on rectangular grids, to unstructured grids and general Hamilton-Jacobi equations. Convergence and error analysis will be carried out. The fact that the fast sweeping method for a nonlinear problem converges in a finite number of iterations is a remarkable result. Further exploration of this method in the general framework of iterative methods will not only provide efficient numerical methods for may important applications but will also shed insight for constructing iterative methods for other nonlinear problems. The above research projects will involve interdisciplinarycollaborations and will be integrated with educationat different levels.Numerical computations play a crucial role in modern science and technology while development of efficient and robust numerical algorithms is the underlying basic task. This project is aimed to the development and analysis of efficient numerical algorithms for two classes of challenging problems with important applications in fluids, materials, biology as well as computer vision, optimal control, and geophysics.

该项目的目标是为两类重要问题开发有效的计算算法。第一个是开发有效的数值方法，用于具有全局动力学的移动界面上的材料传输。主要困难是全局动力学、移动界面和界面上材料分布的耦合。研究人员将开发有效且稳健的方法，这些方法可以（1）跟踪移动界面上的材料传输，（2）将界面动力学与全局动力学耦合。特别是，开发的数值方法将用于研究表面活性剂在两相流中的影响。第二个是分析和扩展快速扫描方法，该方法是最近为矩形网格上的 Eikonal 方程开发的一种高效迭代方法，扩展到非结构网格和一般 Hamilton-Jacobi 方程。将进行收敛和误差分析。非线性问题的快速扫描方法在有限次数的迭代中收敛，这一事实是一个了不起的结果。在迭代方法的一般框架中进一步探索该方法不仅将为可能的重要应用提供有效的数值方法，而且还将为构建其他非线性问题的迭代方法提供见解。上述研究项目将涉及跨学科合作，并将与不同层次的教育相结合。数值计算在现代科学技术中发挥着至关重要的作用，而开发高效、鲁棒的数值算法是其根本任务。该项目旨在开发和分析有效的数值算法，以解决两类具有挑战性的问题，这些问题在流体、材料、生物学以及计算机视觉、最优控制和地球物理学中有重要应用。