**Matrix: Janna/Emilia_923**

Description: geomechanical model for C02 sequestration

(undirected graph drawing) |

Matrix properties | |

number of rows | 923,136 |

number of columns | 923,136 |

nonzeros | 40,373,538 |

structural full rank? | yes |

structural rank | 923,136 |

# of blocks from dmperm | 14,425 |

# strongly connected comp. | 14,425 |

explicit zero entries | 631,668 |

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: 923136 # non-zeroes: 41005206 Problem description: Geomechanical problem The matrix Emilia_923 is obtained from a structural problem discretizing a gas reservoir with tetrahedral Finite Elements. Due to the complex geometry of the geological formation it was not possible to obtain a computational grid characterized by regularly shaped elements. 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. "Geomechanical issues of anthropogenic CO2 sequestration in exploited gas fields", Energy Conversion and Management, 51, pp. 1918-1928, 2010. 2) C. Janna, M. Ferronato. "Adaptive pattern research for block FSAI preconditionig". SIAM Journal on Scientific Computing, to appear.

Ordering statistics: | result |

nnz(chol(P*(A+A'+s*I)*P')) with AMD | 5,317,434,978 |

Cholesky flop count | 1.3e+14 |

nnz(L+U), no partial pivoting, with AMD | 10,633,946,820 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 6,960,196,599 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 12,298,145,622 |

*Note that all matrix statistics (except nonzero pattern symmetry) exclude the 631668 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.
*