**Matrix: Janna/Fault_639**

Description: contact mechanics for model of a faulted gas reservoir

(undirected graph drawing) |

Matrix properties | |

number of rows | 638,802 |

number of columns | 638,802 |

nonzeros | 27,245,944 |

structural full rank? | yes |

structural rank | 638,802 |

# of blocks from dmperm | 21,880 |

# strongly connected comp. | 21,880 |

explicit zero entries | 1,368,620 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | symmetric |

type | real |

structure | symmetric |

Cholesky candidate? | yes |

positive definite? | yes |

author | C. Janna, M. Ferronato |

editor | T. Davis |

date | 2011 |

kind | structural problem |

2D/3D problem? | yes |

Notes:

Authors: Carlo Janna and Massimiliano Ferronato Symmetric Positive Definite Matrix # equations: 638802 # non-zeroes: 28614564 Problem description: contact mechanics The matrix Fault_639 is obtained from a structural problem discretizing a faulted gas reservoir with tetrahedral Finite Elements and triangular Interface Elements. The Interface Elements are used with a Penalty formulation to simulate the faults behaviour. The problem arises from a 3D discretization with three displacement unknowns associated to each node of the grid. Some further information may be found in the following papers: 1) M. Ferronato, G. Gambolati, C. Janna, P. Teatini. "Numerical modelling of regional faults in land subsidence prediction above gas/oil reservoirs", International Journal for Numerical and Analytical Methods in Geomechanics, 32, pp. 633-657, 2008. 2) M. Ferronato, C. Janna, G. Gambolati. "Mixed constraint preconditioning in computational contact mechanics", Computer Methods in Applied Mechanics and Engineering, 197, pp. 3922-3931, 2008. 3) C. Janna, M. Ferronato, G. Gambolati. "Multilevel incomplete factorizations for the iterative solution of non-linear FE problems". International Journal for Numerical Methods in Engineering, 80, pp. 651-670, 2009. 4) C. Janna, M. Ferronato, G. Gambolati. "A Block FSAI-ILU parallel preconditioner for symmetric positive definite linear systems". SIAM Journal on Scientific Computing, 32, pp. 2468-2484, 2010.

Ordering statistics: | result |

nnz(chol(P*(A+A'+s*I)*P')) with AMD | 3,179,862,040 |

Cholesky flop count | 6.4e+13 |

nnz(L+U), no partial pivoting, with AMD | 6,359,085,278 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 3,950,893,717 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 6,902,951,841 |

*Note that all matrix statistics (except nonzero pattern symmetry) exclude the 1368620 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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