ACM Transactions on Mathematical Software (TOMS)
A graph partitioning algorithm by node separators
ACM Transactions on Mathematical Software (TOMS)
Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
Mesh partitioning algorithms for the parallel solution of partial differential equations
Applied Numerical Mathematics - Special issue on parallel scientific computing: from solvers to applications
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Graph partitioning and its applications to scientific computing
Graph partitioning and its applications to scientific computing
Dynamic Network Information Collectionfor Distributed Scientific Application Adaptation
HiPC '02 Proceedings of the 9th International Conference on High Performance Computing
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A number of techniques are described for solving sparse linear systems on parallel platforms. The general approach used is a domain-decomposition type method in which a processor is assigned a certain number of rows of the linear system to be solved. Strategies that are discussed include non-standard graph partitioners, and a forced load-balance technique for the local iterations. A common practice when partitioning a graph is to seek to minimize the number of cut-edges and to have an equal number of equations per processor. It is shown that partitioners that take into account the values of the matrix entries may be more effective.