Department of Computer Science
University of Minnesota at Duluth
320 Heller Hall, 10 University Drive
Duluth, MN 55812-2496, USA
Department of Computer Science and Engineering
University of Minnesota
4-192 EE/CS Building, 200 Union Street S.E.
Minneapolis, MN 55455, USA
Domain-decomposition and multi-level techniques are often formulated for linear systems that arise from the solution of elliptic-type Partial Differential Equations. In this paper, generalizations of these techniques for irregularly structured sparse linear systems are considered. An interesting common approach used to derive successful preconditioners is to resort to Schur complements. In particular, we discuss a multi-level domain decomposition-type algorithm for iterative solution of large sparse linear systems based on independent subsets of nodes. We also discuss a Schur complement technique that utilizes incomplete LU factorizations of local matrices.