the Institute for Theoretical and Engineering Science
Department of Mathematics

University of Houston

Scientific Computing Seminar

Professor Xuejun Xu
LSEC, Institute of Computational Mathematics
Chinese Academy of Sciences, P.O.Box 2719, Beijing 100080, China

Nonoverlapping Schwarz Domain Decomposition Methods

Thursday, January 20
3:00 PM- 4:00 PM
Room 634 S&R1

Abstract: In recent years, a nonoverlapping domain decomposition iterative procedure, which is based on using Robin-type boundary conditions as information transmission conditions on the subdomain interfaces, has been developed and analyzed. The idea of employing Robin-type boundary conditions as interface conditions was first proposed by P.L. Lions. It is known that the convergence rate of this method is $1-O(h)$, where $h$ is mesh size. In this talk, the convergence rate will be improved to $1 - O(h^{1/2} H^{-1/2})$ in certain case by choosing suitable parameter, where $H$ is the subdomain size. Counter examples will be constructed to show that our convergence estimates are sharp, which means that the convergence rate cannot be better than $1 - O(h^{1/2} H^{-1/2})$ in general no matter how parameter is chosen.

This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.