Parallel sparse Gaussian elimination with partial pivoting

In this article, we consider the factorization of a sparse nonsymmetric matrix using Gaussian elimination with partial pivoting on a multiprocessor having a globally-shared memory. The parallel algorithm makes use of a static data structure developed by George, Liu and Ng in [17]. Some numerical experiments on a Sequent Balance 8000 are presented to demonstrate the efficiency of the parallel implementation.

[1]  A. George,et al.  On the Complexity of Sparse $QR$ and $LU$ Factorization of Finite-Element Matrices , 1988 .

[2]  Joseph W. H. Liu,et al.  Reordering sparse matrices for parallel elimination , 1989, Parallel Comput..

[3]  P. Lax Mathematics and computing , 1986 .

[4]  Iain S. Duff,et al.  Full matrix techniques in sparse Gaussian elimination , 1982 .

[5]  Robert Schreiber,et al.  A New Implementation of Sparse Gaussian Elimination , 1982, TOMS.

[6]  Joseph W. H. Liu,et al.  Equivalent sparse matrix reordering by elimination tree rotations , 1988 .

[7]  John K. Reid,et al.  The Multifrontal Solution of Indefinite Sparse Symmetric Linear , 1983, TOMS.

[8]  A. H. Sherman,et al.  Applications of an Element Model for Gaussian Elimination , 1976 .

[9]  G. Stewart Introduction to matrix computations , 1973 .

[10]  Gene H. Golub,et al.  Matrix computations , 1983 .

[11]  Iain S. Duff,et al.  Sparse matrix test problems , 1982 .

[12]  M. Yannakakis Computing the Minimum Fill-in is NP^Complete , 1981 .

[13]  Iain S. Duff Multiprocessing a sparse matrix code on the Alliant FX/8 , 1990 .

[14]  Jochen A. G. Jess,et al.  A Data Structure for Parallel L/U Decomposition , 1982, IEEE Transactions on Computers.

[15]  Joseph W. H. Liu,et al.  Computational models and task scheduling for parallel sparse Cholesky factorization , 1986, Parallel Comput..

[16]  Andrew Harry Sherman,et al.  On the efficient solution of sparse systems of linear and nonlinear equations. , 1975 .

[17]  Joseph W. Liu,et al.  A compact row storage scheme for Cholesky factors using elimination trees , 1986, TOMS.

[18]  Iain S. Duff,et al.  The Multifrontal Solution of Unsymmetric Sets of Linear Equations , 1984 .

[19]  Alan George,et al.  The Evolution of the Minimum Degree Ordering Algorithm , 1989, SIAM Rev..

[20]  A. George,et al.  A data structure for sparse QR and LU factorizations , 1988 .

[21]  Iain S. Duff,et al.  Parallel implementation of multifrontal schemes , 1986, Parallel Comput..

[22]  J. Pasciak,et al.  Computer solution of large sparse positive definite systems , 1982 .

[23]  A. George An automatic one-way dissection algorithm for irregular finite element problems , 1978 .

[24]  A. George Nested Dissection of a Regular Finite Element Mesh , 1973 .

[25]  Joseph W. H. Liu On general row merging schemes for sparse given transformations , 1986 .

[26]  Alan George,et al.  An Optimal Algorithm for Symbolic Factorization of Symmetric Matrices , 1980, SIAM J. Comput..

[27]  Stanley C. Eisenstat,et al.  Software for Sparse Gaussian Elimination with Limited Core Storage. , 1978 .

[28]  A. George,et al.  Symbolic factorization for sparse Gaussian elimination with partial pivoting , 1987 .