A Partitioning Algorithm for Block-Diagonal Matrices With Overlap
We present a graph partitioning algorithm that aims at partitioning a sparse matrix into a block-diagonal form, such that any two consecutive blocks overlap. We denote this form of the matrix as the overlapped block-diagonal matrix. The partitioned matrix is suitable for applying the explicit formulation of Multiplicative Schwarz preconditioner (EFMS) described in [3]. The graph partitioning algorithm partitions the graph of the input matrix into K partitions, such that every partition {Omega}{sub i} has at most two neighbors {Omega}{sub i-1} and {Omega}{sub i+1}. First, an ordering algorithm, such as the reverse Cuthill-McKee algorithm, that reduces the matrix profile is performed. An initial overlapped block-diagonal partition is obtained from the profile of the matrix. An iterative strategy is then used to further refine the partitioning by allowing nodes to be transferred between neighboring partitions. Experiments are performed on matrices arising from real-world applications to show the feasibility and usefulness of this approach.
- Research Organization:
- Ames Laboratory (AMES), Ames, IA
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- AC02-07CH11358
- OSTI ID:
- 941101
- Report Number(s):
- IS-J 7335
- Journal Information:
- Parallel Computing, Journal Name: Parallel Computing Vol. 34; ISSN PACOEJ; ISSN 0167-8191
- Country of Publication:
- United States
- Language:
- English
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