Quebec Mathematical Sciences Colloquium

December 19, 2008 from 16:00 to 18:00 (Montreal/Miami time) On location

Spectral-Galerkin Methods for High-Dimensional PDEs

Colloquium presented by 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 present a new spectral-Galerkin method for non-periodic problems and/or in the whole space. The method is based on two basic ingredients: (i) Choosing the frequencies of the trial functions from the "hyperbolic cross"; (ii) Using a sparse grid or a lattice rule to perform the numerical interpolation/integration. We will present rigorous estimates as well as efficient numerical algorithms for elliptic equations. We will also present some preliminary numerical results for the six-dimensional BGK model.


UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, room 6214