OVERLAPPING DOMAIN DECOMPOSITION ALGORITHMS FOR GENERAL SPARSE MATRICES

Domain decomposition methods for finite element problems using a parti tion based on the underlying finite element mesh have been extensively studied. In this paper, we discuss algebraic extensions of the class of overlapping domain decomposition algorithms for general sparse matr ices. The subproblems are created with an overlapping partition of the graph corresponding to the sparsity structure of the matrix. These al gebraic domain decomposition methods are especially useful for unstruc tured mesh problems. We also discuss some difficulties encountered in the algebraic extension, particularly the issues related to the coarse solver.