Elliptic Problems on Unstructured Meshes

Department of Mathematics

University of California, at Los Angeles

Los Angeles, CA 90024

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.

Contributed April 26, 1994.