Simplified Approaches to Some Nonoverlapping Domain Decomposition Methods

	Jinchao Xu,  Penn State University (xu@math.psu.edu)

An attempt will be made in this talk to present various domain
decomposition methods in a way that is intuitively clear and
technically coherent and concise.  The basic framework used for
analysis is the "parallel subspace correction" or "additive Schwarz"
method, and other simple technical tools include "local-global" and
"global-local" techniques, the formal one is for constructing subspace
preconditioner based on a preconditioner on the whole space whereas
the later one for constructing preconditioner on the whole space based
on a subspace preconditioner.

The domain decomposition methods discussed in this talk fall into two
major categories: one, based on local Dirichlet problems, is related
to the "substructuring method" and the other, based on local Neumann
problems, is related to the "Neumann-Neumann method" and "balancing
method".  All these methods will be presented in a systematic and
coherent manner and the analysis for both two and three dimensional
cases are carried out simultaneously.  In particular, some intimate
relationship between these algorithms are observed and some new
variants of the algorithms are obtained.  

This talk is based on a joint paper with Jun Zou.