New efficient spectral methods for high-dimensional PDEs and<br/><br/>for Fokker-Planck equation of FENE dumbbell model

Wednesday, November 3, 2010 - 10:45am - 11:30am
Keller 3-180
Jie Shen (Purdue University)
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.

We shall also propose a new weighted weak formulation for
the Fokker-Planck equation of FENE dumbbell model, and prove its
well-posedness in weighted Sobolev spaces. Based on the new
formulation, we are able to design simple,
efficient, and unconditionally stable semi-implicit Fourier-Jacobi
schemes for the Fokker-Planck equation of FENE dumbbell model.

It is hoped that the combination of the two new approaches
would make it possible to directly simulate the five or six dimensional
Navier-Stokes Fokker-Planck system.
MSC Code: