**Matrix: Janna/Flan_1565**

Description: 3D model of a steel flange, hexahedral finite elements

(undirected graph drawing) |

Matrix properties | |

number of rows | 1,564,794 |

number of columns | 1,564,794 |

nonzeros | 114,165,372 |

structural full rank? | yes |

structural rank | 1,564,794 |

# of blocks from dmperm | 1 |

# strongly connected comp. | 1 |

explicit zero entries | 3,240,672 |

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: 1564794 # non-zeroes: 117406044 Problem description: Structural problem The matrix Flan_1565 is obtained from a 3D mechanical problem discretizing a steel flange with hexahedral Finite Elements. Due to the regular shape of the mechanical piece, the computational grid is a structured mesh with regularly shaped elements. Three displacement unknowns are associated to each node of the grid. Some further information may be found in the following papers: 1) C. Janna, A. Comerlati, G. Gambolati. "A comparison of projective and direct solvers for finite elements in elastostatics". Advances in Engineering Software, 40, pp. 675-685, 2009. 2) 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 | 3,651,940,140 |

Cholesky flop count | 2.2e+13 |

nnz(L+U), no partial pivoting, with AMD | 7,302,315,486 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 6,488,489,176 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 12,183,623,118 |

*Note that all matrix statistics (except nonzero pattern symmetry) exclude the 3240672 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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