Computational Methods in Mathematics and the Physical Sciences

数学和物理科学的计算方法

• 批准号: 9011083
• 负责人: David Hoffman
• 金额: $ 33.29万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-09-01 至 1994-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9011083&HistoricalAwards=false
• 关键词: Computational; Methods; Mathematics; Physical; Sciences

The principal investigators, David Hoffman and Joel Spruck, will conduct research in differential geometry, calculus of variations and applied Mathematics. This research has a strong computational component, while still addressing problems of current theoretical interest. The computational side two aspects: Implementation of algorithms to solve problems in partial differential equations (arising from physical problems) and scientific graphics. This research involves collaboration with many technical people and scientists from other disciplines, as well as a large number of students and visitors and an active research and training seminar. Critical to these projects has been the creation of a computational laboratory, which has become the core of the Geometry Analysis Numerics and Graphics Center (GANG). Under the technical direction of David Oliver with collaboration of James T. Hoffman, senior graphics programmer, the laboratory is not only supporting high level scientific research, but also producing graphics tools for other sites and providing vital technical assistance to mathematicians and scientists with the need for aid scientific visualization. Among the active research projects are: construction of periodic minimal surfaces; investigation of block copolymer interfaces influenced by boundary constraints; computational fluid dynamics; computational algorithms for plasma confinement; and theoretical and numerical investigation of motion by mean curvature.

首席研究员大卫·霍夫曼（David Hoffman）和乔尔·斯普鲁克（Joel Spruck）将在微分几何、变分微积分和应用数学方面进行研究。这项研究具有很强的计算成分，同时仍然解决当前理论兴趣的问题。计算方面的两个方面：实现算法来解决偏微分方程中的问题（由物理问题引起）和科学图形。这项研究涉及与许多来自其他学科的技术人员和科学家的合作，以及大量的学生和访客，以及一个活跃的研究和培训研讨会。这些项目的关键是创建了一个计算实验室，它已成为几何分析、数值和图形中心（GANG）的核心。在David Oliver的技术指导下，在高级图形程序员James T. Hoffman的合作下，该实验室不仅支持高水平的科学研究，而且还为其他网站制作图形工具，并为需要辅助科学可视化的数学家和科学家提供重要的技术援助。活跃的研究项目有：周期最小曲面的构造；边界约束对嵌段共聚物界面影响的研究计算流体力学；等离子体约束的计算算法；以及平均曲率对运动的理论和数值研究。