报 告 人：Martin J. Gander
报告地点：数学与统计学院104室
报告时间：2014年11月15日星期六10:00
报告简介：It is well known that for domain decomposition methods to be scalable one needs to add a coarse grid. Without, the convergence of the subdomain iterations becomes slower and slower, the more processors, and hence subdomains, one uses. There are well established convergence results for these so called two level methods, for both overlapping and non-overlapping methods. These results however always contain constants which remain unspecified. We explain in this talk how specific choices of coarse space components influence these constants. We start with a simple, one dimensional model problem and develop a coarse space correction which leads together with a Schwarz method to convergence after one coarse correction step. This needs both specific placement of grid points, and well chosen shape functions for the coarse grid correction. We then show that approximations already lead to very good coarse grid corrections, and how this idea can be generalized to two dimensional problems. Next, we show that also interface operators can contain a coarse space component. In particular we will show a domain decomposition method which converges in two iterations independently of the subdomain decomposition, i.e. even if cross points are present. We conclude by an algebraic version for banded matrices, and show an outlook on future work.
主讲人简介：
Martin J. GANDER is a full professor at department of mathematics, University of Geneva, Switzerland; and an adjunct professor of Mathematics at McGill University, Montreal, Canada. He received Diploma (M.S.) in computer science from ETH Zürich (Switzerland) at 1993, M.S. in Mathematics from Stanford University (USA) at 1995, and Ph.D. in Scientific Computing and Computational Mathematics from Stanford University (USA) at 1997. His scientific interests are Domain Decomposition Methods, Waveform Relaxation Methods, Parallel Space Time Methods, Preconditioning, etc. From 2006 to 2011, he was in the editorial board of SIAM Review. Now he is in the editorial boards for seven scientific journals, e.g. SIAM Journal on Scientific Computing, Numerical Algorithms. In addition, he is the president of the International Scientific Committee on Domain Decomposition Methods. Up to now, he has published more than 100 papers in peer-reviewed journals and conference proceedings, such as SIAM Rev., SIAM J. Sci. Comput., SIAM J. Numer. Anal., SIAM J. Matrix Anal., Math. Comp., J. Comput. Acoust., BIT. He is cited for 727 times by 409 authors in the MR citation database (up to Oct. 20, 2014).
