Collaborative Research-ITR-High Order Partial Differential Equations: Theory, Computational Tools, and Applications in Image Processing, Computer Graphics, Biology, and Fluids

协作研究-ITR-高阶偏微分方程：理论、计算工具以及在图像处理、计算机图形学、生物学和流体中的应用

• 批准号: 0321917
• 负责人: Stanley Osher
• 金额: $ 70万
• 依托单位: University of California-Los Angeles
• 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: 2003-09-15 至 2009-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0321917&HistoricalAwards=false
• 关键词: Collaborative; Research; ITR; Order; Partial

This project seeks to develop a comprehensive research and education program in the area of computationalmethods and simulations of physical systems described by high order Partial Differential Equations (PDEs). The program will unify algorithmic, visualization, theoretical, and experimental efforts as well as address applications in areas of science and technology, including computer graphics, image processing, biology, and fluids.Intellectual merit of the proposed activityThis project advances knowledge in the area of high order PDEs, with particular emphasis on curved surface data, and produces enabling technology to address fundamental problems in biology, image processing, computer graphics, and fluids in general. The novel science is in the computationaltechniques, experimental research, and diverse applications addressed by a multi-disciplinary team. Thisproject brings together the five fields of computer science, applied mathematics, mechanical engineering, physics, and electrical and computer engineering.Broader impacts of the proposed activityWith the increasing interest in high order PDEs, the computational tools and experience resulting from this project impact beyond the particular applications in this proposal. Students will receive unusually broadinterdisciplinary training and the workshop planned further brings experts from different fields together. New public domain software incorporating the developed algorithms enables researchers from different fields using higher order PDEs to perform state-of-the-art numerical simulations and graphics rendering of their application of interest.Educational initiatives of this research program include: (1) new interdisciplinary training of graduate students and postdocs through co-mentoring by PIs in different fields; (2) new interdisciplinary courses in computer graphics, numerical analysis, and modeling/simulation of physical phenomena described by higher order PDEs; (3) a workshop bringing together for the first time diverse scientific researchers using high order PDEs.

该项目旨在在计算方法和高阶偏微分方程（PDES）描述的物理系统的模拟领域制定全面的研究和教育计划。 The program will unify algorithmic, visualization, theoretical, and experimental efforts as well as address applications in areas of science and technology, including computer graphics, image processing, biology, and fluids.Intellectual merit of the proposed activityThis project advances knowledge in the area of​​ high order PDEs, with particular emphasis on curved surface data, and produces enabling technology to address fundamental problems in biology, image processing, computer graphics, and液体一般。新颖的科学是由多学科团队解决的计算技术，实验研究和各种应用。 ThisProject汇集了计算机科学，应用数学，机械工程，物理学以及电气和计算机工程的五个领域。拟议活动的影响力对高级PDES的兴趣日益增加，该项目超出该提案中特定应用程序超出该项目的影响。学生将接受异常广泛的学科培训，研讨会计划进一步将不同领域的专家聚集在一起。结合了已发达算法的新的公共领域软件使来自不同领域的研究人员使用高级PDE进行了最先进的数值模拟和图形渲染的图形。 （2）计算机图形学，数值分析以及对高级PDES描述的物理现象的建模/模拟的新跨学科课程； （3）一个研讨会首次使用高级PDE汇集了多样化的科学研究人员。