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## A preliminary analysis of the out-of-core solution phase of a parallel multifrontal approach (2006)

Citations: | 6 - 2 self |

### Citations

651 |
Direct methods for sparse matrices
- Duff, Erisman, et al.
- 1986
(Show Context)
Citation Context ...onsider a parallel out-of-core context, and secondly we focus on the performance of the solve phase. 1 Introduction We are interested in solving large sparse linear systems Ax = b with direct methods =-=[6]-=-, in a parallel limited memory environment. Indeed one main limitation in the use of sparse direct methods comes from the need to store the matrix factors that has often many more entries (10 to 100 t... |

302 |
The multifrontal solution of indefinite sparse symmetric linear systems
- Duff, Reid
- 1983
(Show Context)
Citation Context ...f sparse direct methods comes from the need to store the matrix factors that has often many more entries (10 to 100 times) than the original matrix. In this context, an out-of-core (OOC) multifrontal =-=[7, 8]-=- approach is considered. Here the complete matrix of factors is written to disk during the factorization phase, as a sequence of blocks (so called factor blocks). Overlapping communications and I/O wi... |

257 | A fully asynchronous multifrontal solver using distributed dynamic scheduling
- Amestoy, Duff, et al.
- 2001
(Show Context)
Citation Context ...des (simultaneously or not) then it is even more critical. In this paper, we focus on the performance of the solution phase. We first recall in Section 2 the main features of our target solver (MUMPS =-=[2]-=-,[3],[4]) and fully describe the in-core distributed memory solution phase (never done in previous publications related to MUMPS). Then we explain how it has been adapted to the out-of-core context ∗ ... |

202 |
The role of elimination trees in sparse factorization
- Liu
- 1990
(Show Context)
Citation Context ...symmetric case). • The solution phase performs a forward and backward substitution and, optionally, performs iterative refinement to improve the solution. Multifrontal methods use an elimination tree =-=[9]-=- to represent the dependencies of the computations. Each node of this tree is associated with a frontal matrix that is assembled (summed) by contributions from the children and the original matrix. In... |

185 | Multifrontal parallel distributed symmetric and unsymmetric solvers - Amestoy, Duff, et al. - 2000 |

168 | Scalapack: a portable linear algebra library for distributed memory computers - design issues and performance
- Blackford, Choi, et al.
- 1996
(Show Context)
Citation Context ...any slave processes will be used to process this node. Type3 node: block cyclic 2D distribution of the frontal matrix — reserved only for the root node, if it is large enough. In this case, ScaLAPACK =-=[5]-=- is used on the node. P0 P1 P0 Type 3 P2 P0 P3 P2 P1 P0 − 2D block cyclic parallelism Type 2 P3 P1 P2 P0 P1 P2 P3 P0 P1 P2 − irregular 1D decomposition − sequential processing of the subtree Figure 2:... |

137 | S.: Hybrid scheduling for the parallel solution of linear systems
- Amestoy, Guermouche, et al.
- 2006
(Show Context)
Citation Context ...ultaneously or not) then it is even more critical. In this paper, we focus on the performance of the solution phase. We first recall in Section 2 the main features of our target solver (MUMPS [2],[3],=-=[4]-=-) and fully describe the in-core distributed memory solution phase (never done in previous publications related to MUMPS). Then we explain how it has been adapted to the out-of-core context ∗ This wor... |

89 |
The multifrontal solution of unsymmetric sets of linear equations
- Duff, Reid
- 1984
(Show Context)
Citation Context ...f sparse direct methods comes from the need to store the matrix factors that has often many more entries (10 to 100 times) than the original matrix. In this context, an out-of-core (OOC) multifrontal =-=[7, 8]-=- approach is considered. Here the complete matrix of factors is written to disk during the factorization phase, as a sequence of blocks (so called factor blocks). Overlapping communications and I/O wi... |

34 | The design and implementation of a new out-of-core sparse Cholesky factorization method
- Rotkin, Toledo
(Show Context)
Citation Context ...solution phase. Two different approaches are presented to read data from the disk, with a discussion on the advantages and the drawbacks of each one. Our work differs and extends the work of [10] and =-=[11]-=- because firstly we consider a parallel out-of-core context, and secondly we focus on the performance of the solve phase. 1 Introduction We are interested in solving large sparse linear systems Ax = b... |

23 | Efficient methods for out-of-core sparse Cholesky factorization
- Rothberg, Schreiber
- 1999
(Show Context)
Citation Context ...fficient solution phase. Two different approaches are presented to read data from the disk, with a discussion on the advantages and the drawbacks of each one. Our work differs and extends the work of =-=[10]-=- and [11] because firstly we consider a parallel out-of-core context, and secondly we focus on the performance of the solve phase. 1 Introduction We are interested in solving large sparse linear syste... |

11 |
A preliminary out-of-core extension of a parallel multifrontal solver
- Agullo, Guermouche, et al.
- 2006
(Show Context)
Citation Context ... disk during the factorization phase, as a sequence of blocks (so called factor blocks). Overlapping communications and I/O with computations during the factorization phase is an important issue (see =-=[1]-=-), but is not the scope of this work . During the subsequent phase (forward and backward solutions, the so called solve phase) we have to load the factor blocks from the local disks of the computer to... |