Recent advances in direct methods for solving unsymmetric sparse systems of linear equations
ACM Transactions on Mathematical Software (TOMS)
Recent Progress in General Sparse Direct Solvers
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
An Experimental Comparison of some Direct Sparse Solver Packages
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
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
Cache-conscious performance optimization for similarity search
Proceedings of the 36th international ACM SIGIR conference on Research and development in information retrieval
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Static symbolic factorization coupled with supernode partitioning and asynchronous computation scheduling can achieve high gigaflop rates for parallel sparse LU factorization with partial pivoting. This paper studies properties of elimination forests and uses them to optimize supernode partitioning/amalgamation and execution scheduling. It also proposes supernodal matrix multiplication to speed up kernel computation by retaining the BLAS-3 level efficiency and avoiding unnecessary arithmetic operations. The experiments show that our new design with proper space optimization, called S+, improves our previous solution substantially and can achieve up to 10 GFLOPS on 128 Cray T3E 450MHz nodes.