ylfink@water.waterloo.edu (ylfink) (04/04/88)
DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF WATERLOO
SEMINAR ACTIVITIES
SCIENTIFIC COMPUTATION SEMINAR
- Thursday, April 7, 1988
Professor Olof Widlund of New York University, will
speak on ``Domain Decomposition and Iterative
Refinement Algorithms for Finite Element Problems''.
TIME: 4:00 PM
ROOM: MC 5097
ABSTRACT
In the last few years, there has been a considerable
development of so called iterative substructuring
methods, in which the domain of an elliptic problem is
partitioned into non overlapping subregions. In
particular, a number of algorithms have been designed
for which the rate of convergence varies very slowly
with the number of degrees of freedom as well as with
the number of subregions. In each of the iteration
steps, problems on each subregions are solved, and the
rate of convergence is often enhanced by using a
conjugate gradient method.
The oldest of all domain decomposition methods is
probably the alternating method due to Schwarz. It was
introduced already in 1870. In that method the
subdomains overlap. In this talk, we will first
demonstrate that there is a similar ``additive''
algorithm, which shows considerable promise for
parallel computers. A general framework for the
analysis of this method will be introduced.
Applications are then given which show how fast domain
decomposition methods and iterative refinement
algorithms can be designed. It is also shown that
Yserentant's hierarchical basis function method can be
fit into this framework. We note that a number of
algorithmic ideas and technical tools have been
borrowed from the earlier work on iterative
substructuring methods.