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)|
|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
|Date:||11 / 02 / 2007|
|Time:||03:35pm - 04:25pm|