Parallel implementation of multifrontal schemes
Parallel Computing
Evaluation of orderings for unsymmetric sparse matrics
SIAM Journal on Scientific and Statistical Computing
Use of the P4 and P5 algorithms for in-core factorization of sparse matrices
SIAM Journal on Scientific and Statistical Computing
Solving general sparse linear systems using conjugate gradient-type methods
ICS '90 Proceedings of the 4th international conference on Supercomputing
On Algorithms for Obtaining a Maximum Transversal
ACM Transactions on Mathematical Software (TOMS)
Algorithm 575: Permutations for a Zero-Free Diagonal [F1]
ACM Transactions on Mathematical Software (TOMS)
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Orderings for Parallel Sparse Symmetric Factorization
Proceedings of the Third SIAM Conference on Parallel Processing for Scientific Computing
A Large-Grain Parallel Sparse System Solver
Proceedings of the Fourth SIAM Conference on Parallel Processing for Scientific Computing
A parallel algorithm for sparse unsymmetric lu factorization
A parallel algorithm for sparse unsymmetric lu factorization
Efficient Sparse LU Factorization with Partial Pivoting on Distributed Memory Architectures
IEEE Transactions on Parallel and Distributed Systems
Elimination forest guided 2D sparse LU factorization
Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures
Sparse LU factorization with partial pivoting on distributed memory machines
Supercomputing '96 Proceedings of the 1996 ACM/IEEE conference on Supercomputing
Parallel sparse LU factorization on second-class message passing platforms
Proceedings of the 19th annual international conference on Supercomputing
Parallel sparse LU factorization on different message passing platforms
Journal of Parallel and Distributed Computing
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In this paper, a nonsymmetric sparse linear system solver based on the exploitation of multilevel parallelism is proposed. One of the main issues addressed is the application of tearing techniques to enhance large grain parallelism in a manner that maintains reasonable stability. This is accomplished by a combination of a novel reordering technique (H*) and pivoting strategy. The large grain parallelism exposed by the reordering is combined with medium (various parallel row updates strategies) and fine grain (vectorization) parallelism to allow adaptation to a wide range of multiprocessor architectures. Experimental results are presented which show the effectiveness of the reordering, as well as the stability and efficiency of the solver.