CPM Seminar

Fast Spectral Methods for Scientific and Engineering Computation

Jie Shen

Department of Mathematics
Purdue University

In recent years, spectral methods have become increasingly popular among computational scientists and engineers because of their superior accuracy and efficiency when properly implemented. In this talk, I shall present fast spectral-Galerkin algorithms for some prototypical partial differential equations. These spectral-Galerkin algorithms have computational complexities which are comparable to those of finite difference and finite element algorithms, yet they are capable of providing much more accurate results with a significantly smaller number of unknowns. I shall illustrate applications of these fast spectral-Galerkin algorithms to a number of scientific and engineering problems, including, nonlinear wave equations, nonllinear Schrodinger equations and mutli-phase complex fluids.