A graph partitioning algorithm by node separators
ACM Transactions on Mathematical Software (TOMS)
Computing the block triangular form of a sparse matrix
ACM Transactions on Mathematical Software (TOMS)
Multilevel k-way partitioning scheme for irregular graphs
Journal of Parallel and Distributed Computing
Hypergraph-Partitioning-Based Decomposition for Parallel Sparse-Matrix Vector Multiplication
IEEE Transactions on Parallel and Distributed Systems
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
An Implementation of a Pseudoperipheral Node Finder
ACM Transactions on Mathematical Software (TOMS)
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Implementing Hager's exchange methods for matrix profile reduction
ACM Transactions on Mathematical Software (TOMS)
A linear-time heuristic for improving network partitions
DAC '82 Proceedings of the 19th Design Automation Conference
Fast optimal load balancing algorithms for 1D partitioning
Journal of Parallel and Distributed Computing
An explicit formulation of the multiplicative Schwarz preconditioner
Applied Numerical Mathematics
A parallel solution of large-scale heat equation based on distributed memory hierarchy system
ICA3PP'10 Proceedings of the 10th international conference on Algorithms and Architectures for Parallel Processing - Volume Part II
| Hi-index | 0.00 |
We present an algorithm for partitioning a sparse matrix into a matrix that has blocks on the diagonal such that two consecutive blocks can overlap. We refer to this form of the matrix as block diagonal matrix with overlap. The partitioned matrix is suitable for applying the explicit formulation of multiplicative Schwarz (EFMS) [G.A. Atenekeng Kahou, E. Kamgnia, B. Philippe, An explicit formulation of the multiplicative Schwarz preconditioner, Journal of Applied Numerical Mathematics 57 (2007) 1197-1213] used as a preconditioner for solving a sparse unsymmetric system of linear equations Ax=b. The proposed algorithm partitions the graph of the matrix A into k parts such that every part V"i has connecting edges with at most two neighbors V"i"-"1 and V"i"+"1. First, an ordering algorithm that reduces the profile of the matrix, and an initial block-diagonal partition with overlap is obtained. Second, an iterative strategy is used to further refine the partitioning by allowing vertices to be moved between partitions. Experiments performed on real-world matrices show the usefulness of this approach.