**Matrix: Janna/Long_Coup_dt6**

Description: 3D coupled consolidation problem (geological formation)

(undirected graph drawing) |

Matrix properties | |

number of rows | 1,470,152 |

number of columns | 1,470,152 |

nonzeros | 84,422,970 |

structural full rank? | yes |

structural rank | 1,470,152 |

# of blocks from dmperm | 39,045 |

# strongly connected comp. | 39,045 |

explicit zero entries | 2,666,022 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | symmetric |

type | real |

structure | symmetric |

Cholesky candidate? | no |

positive definite? | no |

author | C. Janna, M. Ferronato |

editor | T. Davis |

date | 2012 |

kind | structural problem |

2D/3D problem? | yes |

Notes:

Authors: Carlo Janna and Massimiliano Ferronato Symmetric Indefinite Matrix # equations: 1,470,152 # non-zeroes: 87,088,992 Problem description: Coupled consolidation problem The matrix Long_Coup is obtained from a 3D coupled consolidation problem of a geological formation discretized with tetrahedral Finite Elements. Due its complex geometry it was not possible to obtain a computational grid characterized by regularly shaped elements. The copuled consolidation problem gives rise to a matrix having 4 unknowns associated to each node: the first three are displacement unknowns, the fourth is a pressure. Coupled consolidation is a transient problem with the matrix ill-conditioning strongly depending on the time step size. We provide a relatively simple problem, "dt0" with a time step size of 10^0 seconds, and a more difficult one, "dt6" with a time step of 10^6 seconds. The two Long_Coup_* matrices are symmetric indefinite. Further information may be found in the following papers: 1) C. Janna, M. Ferronato, G. Gambolati. "Parallel inexact constraint preconditioning for ill-conditioned consolidation problems". Computational Geosciences, submitted. 2) M. Ferronato, L. Bergamaschi, G. Gambolati. "Performance and robustness of block constraint preconditioners in FE coupled consolidation problems". International Journal for Numerical Methods in Engineering, 81, pp. 381-402, 2010. 3) L. Bergamaschi, M. Ferronato, G. Gambolati. "Mixed constraint preconditioners for the iterative solution to FE coupled consolidation equations". Journal of Computational Physics, 227, pp. 9885-9897, 2008. 4) L. Bergamaschi, M. Ferronato, G. Gambolati. "Novel preconditioners for the iterative solution to FE-discretized coupled consolidation equations". Computer Methods in Applied Mechanics and Engineering, 196, pp. 2647-2656, 2007.

Ordering statistics: | result |

nnz(chol(P*(A+A'+s*I)*P')) with AMD | 14,265,014,032 |

Cholesky flop count | 6.1e+14 |

nnz(L+U), no partial pivoting, with AMD | 28,528,557,912 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 15,800,834,415 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 28,211,132,315 |

*Note that all matrix statistics (except nonzero pattern symmetry) exclude the 2666022 explicit zero entries.
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*For a description of the statistics displayed above,
click here.
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*Maintained by Tim Davis, last updated 12-Mar-2014.Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.
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