PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Jinchao Xu.

Title:New results on overlapping Schwarz methods
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Olof Widlund (Courant)
Abstract:
New results have recently been obtained concerning the classical two-level additive Schwarz preconditioners. In the theory for domain decomposition methods, we have previously often assumed that each subdomain is the union of a small set of coarse triangles or tetrahedra. In this study, we present extensions of the existing theory to accommodates subdomains with much less regular shape. One important goal is to extend our analytic tools to problems on subdomains that might not even be Lipschitz and to characterize the rates of convergence of our methods in terms of a few, easy to understand, geometrical parameters of the subregions. We believe that this goal now has been reached fully for scalar elliptic and linear elasticity problems in two dimensions. We have also designed a new family of overlapping Schwarz methods, which in a certain sense is a hybrid algorithm since we borrow and extend coarse spaces from iterative substructuring methods. Methods based on such choices are known to be very robust even in the presence of large local changes of the materials being modeled by the finite element models. An extra attraction is that the overlapping Schwarz methods can be applied directly to problems where the stiffness matrix is available only in its fully assembled form. Important progress has also been made on almost incompressible elasticity and mixed finite element models. One of our results is the first of its kind for this family of saddle point problems and overlapping Schwarz methods. Our work has been done in close collaboration with Clark R. Dohrmann of Sandia National Laboratories, NM and Axel Klawonn and Oliver Rheinbach of the University of Duisburg-Essen, Germany.

Room Reservation Information

Room Number:MB106
Date:11 / 02 / 2007
Time:03:35pm - 04:25pm