A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Parallel unsymmetric-pattern multifrontal sparse LU with column preordering
ACM Transactions on Mathematical Software (TOMS)
PFunc: modern task parallelism for modern high performance computing
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
A shared- and distributed-memory parallel sparse direct solver
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
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We present algorithms for the symbolic and numerical factorization phases in the direct solution of sparse unsymmetric systems of linear equations. We have modified a classical symbolic factorization algorithm for unsymmetric matrices to inexpensively compute minimal elimination structures. We give an efficient algorithm to compute a near-minimal data-dependency graph for unsymmetric multifrontal factorization that is valid irrespective of the amount of dynamic pivoting performed during factorization. Finally, we describe an unsymmetric-pattern multifrontal algorithm for Gaussian elimination with partial pivoting that uses the task- and data-dependency graphs computed during the symbolic phase. These algorithms have been implemented in WSMP---an industrial strength sparse solver package---and have enabled WSMP to significantly outperform other similar solvers. We present experimental results to demonstrate the merits of the new algorithms.