Fast Spectral Methods and their Applications

Purdue University, West Lafayette IN

Investigators

Abstract

The focus of this project is to design accurate, fast and robust spectral methods for solving a large class of partial differential equations, and apply them to investigate several important problems of current interest. More precisely, it is proposed to develop (i) adaptive sparse spectral methods for solving a class of higher-dimensional problems; (ii) spectrally-accurate schemes in space-time for a class of parabolic type PDEs; (iii) robust and accurate spectral methods for electromagnetic scattering, particularly for layered medium and with higher wave numbers; and (iv) to apply the proposed fast and accurate spectral methods to investigate emerging problems in fluid dynamics and materials science such as drop formation & filament breakup and ferroelectric & multiferroic nanostructures in advanced materials processing. It is expected that the proposed numerical simulations will enable us to handle challenging problems having stringent accuracy and/or memory requirements with a reasonable cost in CPU and turn-around time, contribute towards better understandings of the complex physical and mathematical problems, and provide valuable information for the design of advanced materials and on the rheological and hydrodynamic properties of complex fluids. Another important goal of this project is to engage graduate students in learning necessary skills of computational and applied mathematics so that they can pursue a successful career in sciences and engineering.