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
基本信息
- 批准号:0513073
- 负责人:
- 金额:$ 18万
- 依托单位:
- 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:
- 关键词:
项目摘要
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.
这个项目的目标是为两类重要的问题开发有效的计算算法。第一个是发展有效的数值方法,材料输运的移动界面与全球动力学。其主要难点是整体动力学、运动界面和界面上物质分布的耦合。研究人员将开发有效和强大的方法,可以(1)跟踪移动界面上的物质输运,(2)耦合界面动力学与全局动力学。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作用。第二是分析和推广快速扫描方法,这是最近发展的一种有效的迭代方法,在矩形网格上的Eikonal方程,非结构网格和一般的Hamilton-Jacobi方程。并进行了收敛性和误差分析。非线性问题的快速扫描法在有限次迭代中收敛是一个显著的结果。在迭代方法的一般框架下对这种方法的进一步探索不仅将为可能的重要应用提供有效的数值方法,而且还将为构造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,而开发高效和鲁棒的数值算法是其基本任务。该项目旨在为两类具有挑战性的问题开发和分析有效的数值算法,这些问题在流体,材料,生物学以及计算机视觉,最优控制和物理学中具有重要应用。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Hong-Kai Zhao其他文献
Hong-Kai Zhao的其他文献
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{{ truncateString('Hong-Kai Zhao', 18)}}的其他基金
Learning Partial Differential Equation (PDE) and Beyond
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2309551 - 财政年份:2023
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$ 18万 - 项目类别:
Continuing Grant
Intrinsic Complexity of Random Fields and Its Connections to Random Matrices and Stochastic Differential Equations
随机场的内在复杂性及其与随机矩阵和随机微分方程的联系
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2048877 - 财政年份:2020
- 资助金额:
$ 18万 - 项目类别:
Standard Grant
Computational Forward and Inverse Radiative Transfer
计算正向和反向辐射传输
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2012860 - 财政年份:2020
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$ 18万 - 项目类别:
Standard Grant
Intrinsic Complexity of Random Fields and Its Connections to Random Matrices and Stochastic Differential Equations
随机场的内在复杂性及其与随机矩阵和随机微分方程的联系
- 批准号:
1821010 - 财政年份:2018
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$ 18万 - 项目类别:
Standard Grant
Shape and data analysis using computational differential geometry
使用计算微分几何进行形状和数据分析
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1418422 - 财政年份:2014
- 资助金额:
$ 18万 - 项目类别:
Standard Grant
A new approximation for effective Hamiltonians
有效哈密顿量的新近似
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1115698 - 财政年份:2011
- 资助金额:
$ 18万 - 项目类别:
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0811254 - 财政年份:2008
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$ 18万 - 项目类别:
Standard Grant
Applications of Variational Level Set Methods to Some Multiphase Problems
变分水平集方法在一些多相问题中的应用
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9706566 - 财政年份:1997
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$ 18万 - 项目类别:
Standard Grant
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