Fast Spectral-Galerkin Methods for High-Dimensional PDEs and Applications to the electronic Schrodinger equation

Applied and Computational Mathematics Seminar
Monday, October 31, 2011 - 2:00pm
1 hour (actually 50 minutes)
Skiles 006
Purdue University, Department of Mathematics
Many scientific, engineering and financial applications require solving high-dimensional PDEs. However, traditional tensor product based algorithms suffer from the so called "curse of dimensionality".We shall construct a new sparse spectral method for high-dimensional problems, and present, in particular,  rigorous error estimates as well as efficient numerical algorithms for  elliptic equations in both bounded and unbounded domains.As an application, we shall use the proposed sparse spectral method to solve the N-particle electronic  Schrodinger equation.