**Matrix: GHS_psdef/s3dkq4m2**

Description: FEM, cylindrical shell, 150x100 quad. mesh, R/t=1000

(undirected graph drawing) |

Matrix properties | |

number of rows | 90,449 |

number of columns | 90,449 |

nonzeros | 4,427,725 |

structural full rank? | yes |

structural rank | 90,449 |

# of blocks from dmperm | 1 |

# strongly connected comp. | 1 |

explicit zero entries | 393,166 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | symmetric |

type | real |

structure | symmetric |

Cholesky candidate? | yes |

positive definite? | yes |

author | R. Kouhia |

editor | R. Boisvert, R. Pozo, K. Remington, B. Miller, R. Lipman, R. Barrett, J. Dongarra |

date | 1997 |

kind | structural problem |

2D/3D problem? | yes |

Additional fields | size and type |

coord | full 90449-by-3 |

Notes:

% %FILE s3dkq4m2.mtx %TITLE Cyl shell R/t=1000 unif 150x100 quad mesh DKQ elem with drill rot %KEY s3dkq4m2 % % %CONTRIBUTOR Reijo Kouhia (reijo.kouhia@hut.fi) % %REFERENCE M. Benzi, R. Kouhia, M.Tuma: An assesment of some % preconditioning techniques in shell problems % Technical Report LA-UR-97-3892, Los Alamos National Laboratory % %BEGIN DESCRIPTION % Matrix from a static analysis of a cylindrical shell % Radius to thickness ratio R/t = 1000 % Length to radius ratio R/L = 1 % One octant discretized with uniform 150 x 100 quadrilateral mesh % element: % facet-type shell element where the bending part is formulated % using the discrete Kirchhoff quadrilateral (Lyons-Crisfield version), % the membrane part includes drilling rotations using % the Hughes-Brezzi formulation with (regularizing parameter = G/1000, % where G is the shear modulus) % full 2x2 Gauss-Legendre integration % -------------------------------------------------------------------------- % Note: % The sparsity pattern of the matrix is determined from the element % connectivity data assuming that the element matrix is full. % Since this case the material model is linear isotropically elastic % and the FE mesh is uniform there exist some zeros. % Since the removal of those zero elements is trivial % but the reconstruction of the current sparsity % pattern is impossible from the sparsified structure without any further % knowledge of the element connectivity, the zeros are retained in this file. % --------------------------------------------------------------------------- %END DESCRIPTION % %

Ordering statistics: | result |

nnz(chol(P*(A+A'+s*I)*P')) with AMD | 27,399,094 |

Cholesky flop count | 1.8e+10 |

nnz(L+U), no partial pivoting, with AMD | 54,707,739 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 50,277,848 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 98,614,571 |

*Note that all matrix statistics (except nonzero pattern symmetry) exclude the 393166 explicit zero entries.
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*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.
*