Some Domain Decomposition Methods for Indefinite
                   Elliptic Problems on Unstructured Meshes

                                Jian Ping Shao
                          Department of Mathematics
                   University of California, at Los Angeles
                            Los Angeles, CA 90024

                                   Abstract

In this paper, we analyze some domain decomposition methods for indefinite
elliptic problems on unstructured meshes.  Our theory requires no assumption
on the shape of the subdomains.  They can have arbitrary shape.  Unlike usual
domain decomposition, the coarse and fine triangulations need not be nested
and quasi-uniform.  Furthermore, the nodes of substructures are not necessary
to be the coarser grids.  This general setting in the domain decomposition
makes us easier to deal with complicated goemetry domain, discontinuous
coefficients and boundary layers.  Moreover, it becomes easier to balance the
work load of each processor in a parallel computer system since we have more
flexibility in the choice of the number of the coarser grids.  We will show
that the domain decomposition methods for indefinite problems on the
unstructured meshes remain optimal convergence rate when the coarser grid size
and subdomain diameters are small enough.