**Matrix: Quaglino/viscoplastic1**

Description: FEM discretization of a viscoplastic collision problem, Alessio Quaglino

(bipartite graph drawing) | (graph drawing of A+A') |

Matrix properties | |

number of rows | 4,326 |

number of columns | 4,326 |

nonzeros | 61,166 |

structural full rank? | yes |

structural rank | 4,326 |

# of blocks from dmperm | 1 |

# strongly connected comp. | 1 |

explicit zero entries | 0 |

nonzero pattern symmetry | 74% |

numeric value symmetry | 0% |

type | real |

structure | unsymmetric |

Cholesky candidate? | no |

positive definite? | no |

author | A. Quaglino |

editor | T. Davis |

date | 2007 |

kind | materials problem |

2D/3D problem? | yes |

Additional fields | size and type |

b | full 4326-by-1 |

C | cell 7-by-1 |

Notes:

The matrix is in the form [A11 A12 ; A21 A22] where A11 and A22 are diagonal. Originally, the matrices in this set were poorly scaled, but this was resolved by a scale factor of the form [A11 A12*e ; A21/e A4] where the scalar e is of magnitude 1e2 but can be 1e6 or 1e7 for a stiff material. The Problem.A matrix is the properly scaled problem. The Problem.aux.C{1:7} matrices have been "unscaled" with a factor e = 10.^(-(1:7)), to give a sequence of matrices that are well scaled to poorly scaled, and thus well conditioned (C{1}) to poorly conditioned (C{7}). This mimics the original poorly scaled and ill- conditioned problem, and may be of interest for those developing algorithms for automatic scaling. From a FEM discretization of a viscoplastic collision problem, Alessio Quaglino.

Ordering statistics: | result |

nnz(chol(P*(A+A'+s*I)*P')) with AMD | 71,771 |

Cholesky flop count | 2.2e+06 |

nnz(L+U), no partial pivoting, with AMD | 139,216 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 705,015 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 1,530,390 |

SVD-based statistics: | |

norm(A) | 73.8743 |

min(svd(A)) | 0.000529054 |

cond(A) | 139635 |

rank(A) | 4,326 |

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

null space dimension | 0 |

full numerical rank? | yes |

singular values (MAT file): | click here |

SVD method used: | s = piro_band_svd (A) |

status: | ok |

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.
*