Joint Diagonalization-Based Spectral Element Approach

基于联合对角化的谱元方法

• 批准号: 1318820
• 负责人: Suchuan Dong
• 金额: $ 18.9万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1318820&HistoricalAwards=false
• 关键词: Joint; Diagonalization; Based; Spectral; Element

This project aims to develop algorithmically scalable high-order numerical techniques. The essential components consist of numerically-constructed one-dimensional basis functions, which correspond to a set of optimal bases in the function space in some sense. Expansion bases for higher dimensions are then developed from such functions. Methods employing these new bases exhibit superior properties in terms of numerical efficiency and algorithmic scalability.The investigator develops techniques that make computer simulations of physical processes both very accurate and very fast. These computer simulations permeate essentially every aspect of modern life. They are indispensable and critical to, for example, the design of airplanes and spacecrafts, discovery and design of new materials, understanding and prediction of severe weather conditions such as tornadoes and hurricanes, understanding and prevention of oil spills. The significance of the project lies in that the techniques developed herein can significantly reduce the time to acquire the solutions in simulations, and simultaneously substantially increase the simulation accuracy.

该项目旨在开发算法可扩展的高阶数值技术。基本成分由数值构造的一维基函数组成，在某种意义上对应于函数空间中的一组最优基。更高维度的扩展基然后从这样的函数发展。采用这些新基地的方法表现出优越的上级性能的数值效率和算法scalability.The调查员开发的技术，使计算机模拟的物理过程都非常准确，非常快。这些计算机模拟基本上渗透到现代生活的各个方面。例如，它们对飞机和航天器的设计、新材料的发现和设计、对龙卷风和飓风等恶劣天气条件的了解和预测、对石油泄漏的了解和预防等都是不可或缺和至关重要的。该项目的意义在于，本文开发的技术可以显着减少时间来获得的解决方案在模拟，同时大大提高了模拟精度。