8月2日 Long Chen 副教授学术报告

发布时间:2013-08-01

报告人：Long Chen, University of California at Irvine

时 间： 8月2日（周五）  下午4：00-5：00

地 点：数学楼210室

Abstract:

Stokes equations can be discretized and the resulting algebraic systems can be solved by many different approaches.  For example, a multigrid method based on Distributive Gauss-Seidel (DGS) relaxation (by A. Brandt ) is known to be an efficient solver for the staggered grid discretization (MAC scheme) of Stokes equations on uniform grids. For more general finite element discretizations of Stokes equations, we will report in this talk a Fast Auxiliary Space Preconditioning (FASP) method which uses a DGS relaxation based on the least squares commutator (LSC) and one W-cycle for a MAC-like scheme as the auxiliary space correction solver. Numerical experiments will also be provided to show the proposed approach results a highly efficient solver for Stokes equations.

In the second part of this talk, we will present fast multilevel methods for the approximate solution of the discrete problems that arise from the discretization of fractional Laplacian. The fractional Laplacian is a nonlocal operator. To localize it, we solve a Dirichlet to a Neumann-type operator via an extension problem. However, this comes at the expense of incorporating one more dimension to the problem, thus motivates our study of multilevel methods. Because of the singularity of the solution, anisotropic elements in the extended variable are needed in order to obtain quasi-optimal error estimates. For this reason, we also consider a multigrid method with a line smoother and obtain nearly uniform convergence rates.

报告人简介：

http://www.math.uci.edu/~chenlong/