Direct methods for sparse matrices
Direct methods for sparse matrices
Solving problems on concurrent processors. Vol. 1: General techniques and regular problems
Solving problems on concurrent processors. Vol. 1: General techniques and regular problems
Circuit Simulation on Shared-Memory Multiprocessors
IEEE Transactions on Computers
Sparse Cholesky factorization on a local-memory multiprocessor
SIAM Journal on Scientific and Statistical Computing
Efficient sparse matrix factorization for circuit simulation on vector supercomputers
DAC '89 Proceedings of the 26th ACM/IEEE Design Automation Conference
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
Computer Methods for Circuit Analysis and Design
Computer Methods for Circuit Analysis and Design
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Effects of partitioning and scheduling sparse matrix factorization on communication and load balance
Proceedings of the 1991 ACM/IEEE conference on Supercomputing
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The problem of reducing the amount of interprocessor communication during the distributed factorization of a sparse matrix on a mesh-connected processor network is investigated. Two strategies are evaluated - 1) use of a fragmented distribution of row/columns of the matrix to limit the number of processors to which each row/column segment is transmitted, and 2) use of the elimination tree to permute the matrix so as to internalize as much of the communication as possible. Empirical evaluation of the schemes using matrices derived from circuit simulation shows significant reduction in the amount of communication for a 64 processor mesh.