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Domain decomposition methods for Finite Element problems using a partition based on the underlying nite element mesh have been extensively studied In this paper we discuss algebraic extensions of the class of overlapping domain decomposition algorithms for general sparse matrices The subproblems are created with an overlapping partition of the graph corresponding to the sparsity structure of the matrix These algebraic domain decomposition methods are especially useful for unstructured mesh problems We also discuss some di culties encountered in the algebraic extension particularly the issues related to the coarse solver

Overlapping Domain Decomposition Algorithms for General Sparse Matrices