**Matrix: Janna/Geo_1438**

Description: geomechanical model of earth crust with underground deformation

(undirected graph drawing) |

Matrix properties | |

number of rows | 1,437,960 |

number of columns | 1,437,960 |

nonzeros | 60,236,322 |

structural full rank? | yes |

structural rank | 1,437,960 |

# of blocks from dmperm | 66,481 |

# strongly connected comp. | 66,481 |

explicit zero entries | 2,920,368 |

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: 1437960 # non-zeroes: 63156690 Problem description: Geomechanical problem The matrix Geo_1438 is obtained from a geomechanical problem discretizing a region of the earth crust subject to underground deformation. The computational domain is a box with an areal extent of 50 x 50 km and 10 km deep consisting of regularly shaped tetrahedral Finite Elements. The problem arises from a 3D discretization with three displacement unknowns associated to each node of the grid. This matrix has been used as a test case in the following paper: 1) 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 | 6,297,700,169 |

Cholesky flop count | 1.2e+14 |

nnz(L+U), no partial pivoting, with AMD | 12,593,962,378 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 7,633,969,695 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 13,733,310,294 |

*Note that all matrix statistics (except nonzero pattern symmetry) exclude the 2920368 explicit zero entries.
*

*For a description of the statistics displayed above,
click here.
*

*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.
*