Overlapping domain decomposition algorithms for general sparse matrices

Xiao Chuan Cai, Yousef Saad

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


Domain decomposition methods for finite element problems using a partition 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 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 difficulties encountered in the algebraic extension, particularly the issues related to the coarse solver.

Original languageEnglish (US)
Pages (from-to)221-237
Number of pages17
JournalNumerical Linear Algebra with Applications
Issue number3
StatePublished - 1996


  • Domain decomposition
  • Graph partitioning
  • Iterative methods
  • Preconditioning
  • Sparse matrix


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