**Matrix: TKK/smt**

Description: 3D model, thermal stress analysis of surface mounted transistor. R Kohia

(undirected graph drawing) |

Matrix properties | |

number of rows | 25,710 |

number of columns | 25,710 |

nonzeros | 3,749,582 |

structural full rank? | yes |

structural rank | 25,710 |

# of blocks from dmperm | 1 |

# strongly connected comp. | 1 |

explicit zero entries | 3,602 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | symmetric |

type | real |

structure | symmetric |

Cholesky candidate? | yes |

positive definite? | yes |

author | R. Kouhia |

editor | T. Davis |

date | 2008 |

kind | structural problem |

2D/3D problem? | yes |

Additional fields | size and type |

b | full 25710-by-1 |

coord | full 25710-by-3 |

Notes:

Matrix problems from Reijo Kouhia, Structural Mechanics, Helsinki University of Technology. http://users.tkk.fi/~kouhia/sparse.html Surface mount transistor, 1704 reduced triquadratic elem, therm stress. This is a stiffness matrix from a thermal stress analysis of a surface mounted transistor. Due to symmetry only one half of the model is discretized in 1704 standard reduced triquadratic elements (20 node serendipity). There are 5 different materials. The stiffness matrix is integrated by 3x3x3 Gaussian quadrature. Separate load vector file is also available. Figure of the FE model can be seen in a separate description, or downloaded as a postscript file from the contributors www-pages. Contributor: Reijo Kouhia, Helsinki University of Technology, Laboratory of Structural Mechanics PO Box 2100, 02015 HUT, Finland e-mail: reijo.kouhia@hut.fi http://www.hut.fi/~kouhia

Ordering statistics: | result |

nnz(chol(P*(A+A'+s*I)*P')) with AMD | 14,601,688 |

Cholesky flop count | 1.4e+10 |

nnz(L+U), no partial pivoting, with AMD | 29,177,666 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 26,940,204 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 65,904,871 |

*Note that all matrix statistics (except nonzero pattern symmetry) exclude the 3602 explicit zero entries.
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SVD-based statistics: | |

norm(A) | 5.29766e+06 |

min(svd(A)) | 0.00333867 |

cond(A) | 1.58676e+09 |

rank(A) | 25,710 |

sprank(A)-rank(A) | 0 |

null space dimension | 0 |

full numerical rank? | yes |

singular values (MAT file): | click here |

SVD method used: | s = svd (full (A)) |

status: | ok |

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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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