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SuperLU DIST: A scalable distributedmemory sparse direct solver for unsymmetric linear systems
 ACM Trans. Mathematical Software
, 2003
"... We present the main algorithmic features in the software package SuperLU DIST, a distributedmemory sparse direct solver for large sets of linear equations. We give in detail our parallelization strategies, with a focus on scalability issues, and demonstrate the software’s parallel performance and sc ..."
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Cited by 144 (18 self)
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We present the main algorithmic features in the software package SuperLU DIST, a distributedmemory sparse direct solver for large sets of linear equations. We give in detail our parallelization strategies, with a focus on scalability issues, and demonstrate the software’s parallel performance and scalability on current machines. The solver is based on sparse Gaussian elimination, with an innovative static pivoting strategy proposed earlier by the authors. The main advantage of static pivoting over classical partial pivoting is that it permits a priori determination of data structures and communication patterns, which lets us exploit techniques used in parallel sparse Cholesky algorithms to better parallelize both LU decomposition and triangular solution on largescale distributed machines.
Design, Implementation and Testing of Extended and Mixed Precision BLAS
, 2001
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Preconditioning highly indefinite and nonsymmetric matrices
 SIAM J. SCI. COMPUT
, 2000
"... Standard preconditioners, like incomplete factorizations, perform well when the coefficient matrix is diagonally dominant, but often fail on general sparse matrices. We experiment with nonsymmetric permutationsand scalingsaimed at placing large entrieson the diagonal in the context of preconditionin ..."
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Cited by 55 (3 self)
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Standard preconditioners, like incomplete factorizations, perform well when the coefficient matrix is diagonally dominant, but often fail on general sparse matrices. We experiment with nonsymmetric permutationsand scalingsaimed at placing large entrieson the diagonal in the context of preconditioning for general sparse matrices. The permutations and scalings are those developed by Olschowka and Neumaier [Linear Algebra Appl., 240 (1996), pp. 131–151] and by Duff and
ARMS: An Algebraic Recursive Multilevel Solver for general sparse linear systems
 Numer. Linear Alg. Appl
, 1999
"... This paper presents a general preconditioning method based on a multilevel partial solution approach. The basic step in constructing the preconditioner is to separate the initial points into two subsets. The first subset which can be termed "coarse" is obtained by using "block" ..."
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Cited by 53 (24 self)
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This paper presents a general preconditioning method based on a multilevel partial solution approach. The basic step in constructing the preconditioner is to separate the initial points into two subsets. The first subset which can be termed "coarse" is obtained by using "block" independent sets, or "aggregates". Two aggregates have no coupling between them, but nodes in the same aggregate may be coupled. The nodes not in the coarse set are part of what might be called the "Fringe" set. The idea of the methods is to form the Schur complement related to the fringe set. This leads to a natural block LU factorization which can be used as a preconditioner for the system. This system is then solver recursively using as preconditioner the factorization that could be obtained from the next level. Unlike other multilevel preconditioners available, iterations between levels are allowed. One interesting aspect of the method is that it provides a common framework for many other technique...
Recent Advances in Direct Methods for Solving Unsymmetric Sparse Systems of Linear Equations
, 2001
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WSMP: Watson sparse matrix package part I—direct solution of symmetric sparse system
 Center, Yorktown Heights
, 2010
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Analysis and comparison of two general sparse solvers for distributed memory computers
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 2001
"... This paper provides a comprehensive study and comparison of two stateoftheart direct solvers for large sparse sets of linear equations on largescale distributedmemory computers. One is a multifrontal solver called MUMPS, the other is a supernodal solver called SuperLU. We describe the main algo ..."
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Cited by 23 (7 self)
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This paper provides a comprehensive study and comparison of two stateoftheart direct solvers for large sparse sets of linear equations on largescale distributedmemory computers. One is a multifrontal solver called MUMPS, the other is a supernodal solver called SuperLU. We describe the main algorithmic features of the two solvers and compare their performance characteristics with respect to uniprocessor speed, interprocessor communication, and memory requirements. For both solvers, preorderings for numerical stability and sparsity play an important role in achieving high parallel efficiency. We analyse the results with various ordering algorithms. Our performance analysis is based on data obtained from runs on a 512processor Cray T3E using a set of matrices from real applications. We also use regular 3D grid problems to study the scalability of the two solvers.
Is 1.7 x 10^10 unknowns the largest finite element system that can be solved today?
 IN SC ’05: PROCEEDINGS OF THE 2005 ACM/IEEE CONFERENCE ON SUPERCOMPUTING
, 2005
"... Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage, and that copies bear this notice and the full citation on the first page. To copy otherwise, ..."
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Cited by 18 (3 self)
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Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage, and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.