Computational Methods in Mathematics and the Physical Sciences

主要研究人员大卫·霍夫曼和乔尔·斯普拉克将进行微分几何、变分和应用数学方面的研究。这项研究具有强大的计算成分，同时仍在解决当前理论上感兴趣的问题。计算方面有两个方面：实现算法来解决偏微分方程组中的问题(由物理问题引起)和科学图形学。这项研究涉及与来自其他学科的许多技术人员和科学家以及大量学生和访问者的合作，以及一次积极的研究和培训研讨会。这些项目的关键是建立一个计算实验室，它已经成为几何分析、数值和图形中心(GANG)的核心。在大卫·奥利弗的技术指导下，在高级图形程序员詹姆斯·T·霍夫曼的合作下，该实验室不仅支持高水平的科学研究，还为其他站点生产图形工具，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。正在进行的研究项目包括：周期极小曲面的构造；受边界约束影响的嵌段共聚物界面的研究；计算流体力学；等离子体约束的计算算法；以及平均曲率运动的理论和数值研究。

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.