Advances in Level Set and Related Methods: New Technology and Applications

水平集及相关方法的进展：新技术与应用

• 批准号: 0074735
• 负责人: Stanley Osher
• 金额: $ 15.5万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-01 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0074735&HistoricalAwards=false
• 关键词: Advances; Level; Set; Related; Methods

NSF Proposal: DMS-0074735 "Advances in Level Set and Related Methods: New Technologies and Applications" Principal Investigator: Stanley J. OsherABSTRACTThe level set method devised by Osher and Sethian in 1988 has proven to be phenomenally successful as a numerical and theoretical device for representing and analyzing the motion of curves in R^2 and surfaces in R^3. A level set calculus has been developed, and recent extensions include the ghost fluid method, convolution generated motion, dynamic surface extension, the variational level set approach, and the motion of higher codimensional objects. Recent applications include multiphase fluid dynamics, the island dynamics model for epitaxial growth, level set based interpolation of unorganized points, and fast methods in image restoration. This work was partially supported by our previous NSF grants. The goal of this proposed research is to extend the technology and the range of applications through the following two projects:(1) Convolution generated motion for filaments.(2) Fast algorithms for steady state geometric Hamilton-Jacobi equations and the induced motion of fronts.The level set method is rapidly becoming the method of choice to simulate on the computer a host of important physical, biological, materials science, image processing, computer vision, electromagnetic and other real world problems. In particular areas of nanotechnology will also be impacted. Improvements of the numerical methods used to simulate these phenomena will ultimately be crucial in the design of computer chips, analysis of explosions, recognition of objects and many other areas of modern technology. This proposal addresses further improvements of the level set and related methods.

美国国家科学基金会建议：DMS-0074735《水平集及相关方法的进展：新技术和应用》主要研究人员：斯坦利·J·奥希尔1988年由Osher和Sethian提出的水平集方法已被证明是一种非常成功的数值和理论工具，用于表示和分析R^2中的曲线和R^3中的曲面的运动。水平集演算已经发展起来，最近的扩展包括幽灵流体方法、卷积生成的运动、动态表面扩展、变分水平集方法和高维物体的运动。最近的应用包括多相流体动力学、外延生长的孤岛动力学模型、基于水平集的无组织点内插以及图像恢复的快速方法。这项工作得到了我们之前的NSF拨款的部分支持。这项研究的目标是通过以下两个项目来扩大技术和应用范围：(1)卷积生成细丝运动。(2)稳态几何Hamilton-Jacobi方程和前沿诱导运动的快速算法。水平集方法正迅速成为在计算机上模拟许多重要的物理、生物、材料科学、图像处理、计算机视觉、电磁和其他现实世界问题的首选方法。特别是纳米技术领域也将受到影响。用于模拟这些现象的数值方法的改进最终将在计算机芯片设计、爆炸分析、物体识别和许多其他现代技术领域发挥关键作用。该提案涉及对水平集和相关方法的进一步改进。