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PSPASES: An Efficient and Scalable Parallel Sparse Direct Solver
 IN PROCEEDINGS OF THE NINTH SIAM CONFERENCE ON PARALLEL PROCESSING FOR SCIENTIFIC COMPUTING
, 1999
"... Many problems in engineering and scientific domains require solving large sparse systems of linear equations, as a computationally intensivesteptowards the final solution. It has long beenachallenge to develop efficient parallel formulations of sparse direct solvers due to several different complex ..."
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Cited by 5 (2 self)
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Many problems in engineering and scientific domains require solving large sparse systems of linear equations, as a computationally intensivesteptowards the final solution. It has long beenachallenge to develop efficient parallel formulations of sparse direct solvers due to several different complex
A Parallel Fast Direct Solver With Applications
"... . The effectiveness and applicability of a parallel fast direct O(N log N) solver for linear systems with block tridiagonal separable coefficient matrices is considered. This solver is applied in the solution of subsonic full potential flows using the Newton linearization and an algebraic fictit ..."
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. The effectiveness and applicability of a parallel fast direct O(N log N) solver for linear systems with block tridiagonal separable coefficient matrices is considered. This solver is applied in the solution of subsonic full potential flows using the Newton linearization and an algebraic
Fast Parallel Direct Solvers For Coarse Grid Problems
 J. Parallel and Distributed Computing
, 1997
"... We develop a fast direct solver for parallel solution of "coarse grid" problems, Ax = b, such as arise when domain decomposition or multigrid methods are applied to elliptic partial differential equations in d space dimensions. The approach is based upon a (quasi) sparse factorization ..."
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We develop a fast direct solver for parallel solution of "coarse grid" problems, Ax = b, such as arise when domain decomposition or multigrid methods are applied to elliptic partial differential equations in d space dimensions. The approach is based upon a (quasi) sparse factorization
Fast direct solvers for elliptic partial differential equations
, 2011
"... The dissertation describes fast, robust, and highly accurate numerical methods for solving boundary value problems associated with elliptic PDEs such as Laplace’s and Helmholtz ’ equations, the equations of elasticity, and timeharmonic Maxwell’s equation. In many areas of science and engineering, ..."
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Cited by 10 (4 self)
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The dissertation describes fast, robust, and highly accurate numerical methods for solving boundary value problems associated with elliptic PDEs such as Laplace’s and Helmholtz ’ equations, the equations of elasticity, and timeharmonic Maxwell’s equation. In many areas of science and engineering, the cost of solving such problems determines what can and cannot be modeled computationally. Elliptic boundary value problems may be solved either via discretization of the PDE (e.g., finite element methods) or by first reformulating the equation as an integral equation, and then discretizing the integral equation. In either case, one is left with the task of solving a system of
Objectoriented design for sparse direct solvers
 Institute for Computer
, 1999
"... Abstract. We discuss the objectoriented design of a software package for solving sparse, symmetric systems of equations (positive definite and indefinite) by direct methods. At the highest layers, we decouple data structure classes from algorithmic classes for flexibility. We describe the important ..."
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Cited by 4 (0 self)
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Abstract. We discuss the objectoriented design of a software package for solving sparse, symmetric systems of equations (positive definite and indefinite) by direct methods. At the highest layers, we decouple data structure classes from algorithmic classes for flexibility. We describe
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 145 (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
The Design of I/OEfficient Sparse Direct Solvers
"... We consider two problems related to I/O: First, find the minimum primary memory size required to factor a sparse, symmetric matrix when permitted to read and write the data exactly once. Second, find the minimum data traffic between core and external memory when permitted to read and write the data ..."
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Cited by 1 (0 self)
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the data (files managed by the program) improves performance significantly over implicit data movement (pages managed by the operating system). Thus this work guides us in designing a software library that implements an external memory sparse solver. 1
The Design of Sparse Direct Solvers using ObjectOriented Techniques
, 1999
"... We describe our experience in designing objectoriented software for sparse direct solvers. We discuss, a library of sparse matrix ordering codes, and, a package that implements the factorization and triangular solution steps of a direct solver. We discuss the goals of our design: managing complex ..."
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Cited by 18 (4 self)
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We describe our experience in designing objectoriented software for sparse direct solvers. We discuss, a library of sparse matrix ordering codes, and, a package that implements the factorization and triangular solution steps of a direct solver. We discuss the goals of our design: managing
SCALABILITY OF SPARSE DIRECT SOLVERS "
"... Abstract. We shall say that a scalable algorithm achieves efficiency that is bounded away from zero as the number of processors and the problem size increase in such a way that the size of the data structures increases linearly with the number of processors. In this paper we show that the columnori ..."
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Abstract. We shall say that a scalable algorithm achieves efficiency that is bounded away from zero as the number of processors and the problem size increase in such a way that the size of the data structures increases linearly with the number of processors. In this paper we show that the columnoriented approach to sparse Cholesky for distributedmemory machines is not scalable. By considering message volume, node contention, and bisection width, one may obtain lower bounds on the time required for communication in a distributed algorithm. Applying this technique to distributed, columnoriented, full Cholesky leads to the conclusion that N (the order of the matrix) must scale with P (the number of processors) so that storage grows like p2. So the algorithm is not scalable. Identical conclusions have previously been obtained by consideration of communication and computation latency on the critical path in the algorithm; these results complement and reinforce that conclusion. For the sparse case, we have experimental measurements that make the same point: for columnoriented distributed methods, the number of gridpoints (which is O(N)) must grow as P _ in order to maintain parallel efficiency bounded above zero. Our sparse matrix results employ the "fanin " distributed scheme, implemented on machines with either a grid or a fattree interconnect using a subtreetosubmachine mapping of the columns.
Results 11  20
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