Joint Diagonalization-Based Spectral Element Approach

该项目旨在开发算法可伸缩的高阶数值技术。本质成分由数值构造的一维基函数组成，它们在某种意义上对应于函数空间中的一组最优基。然后，从这些功能中开发出更高维度的扩展基础。使用这些新的基的方法在数值效率和算法可伸缩性方面表现出优越的特性。研究人员开发了使物理过程的计算机模拟既非常准确又非常快速的技术。这些计算机模拟基本上渗透到现代生活的方方面面。例如，它们对于飞机和宇宙飞船的设计、新材料的发现和设计、对龙卷风和飓风等恶劣天气状况的了解和预测、对石油泄漏的了解和预防都是不可或缺的和关键的。该项目的意义在于，本文所开发的技术可以显著减少在仿真中获得解的时间，同时大幅提高仿真精度。

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.