Joint Diagonalization-Based Spectral Element Approach

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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.