**Matrix: Cylshell/s2rmq4m1**

Description: FEM, cylindrical shell, 30x30 quad. mesh, stabilized MITC4 elements, R/t=100

(undirected graph drawing) |

Matrix properties | |

number of rows | 5,489 |

number of columns | 5,489 |

nonzeros | 263,351 |

structural full rank? | yes |

structural rank | 5,489 |

# of blocks from dmperm | 1 |

# strongly connected comp. | 1 |

explicit zero entries | 17,760 |

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 5489-by-3 |

Notes:

% %FILE s2rmq4m1.mtx %TITLE Cyl shell R/t = 100 unif 30x30 quad mesh stab MITC4 elem with drill rot %KEY s2rmq4m1 % % %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 = 100 % Length to radius ratio R/L = 1 % One octant discretized with uniform 30 x 30 quadrilateral mesh % element: % facet-type shell element where the bending part is formulated % using the stabilized MITC theory (stabilization paramater 0.4) % 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 | 927,079 |

Cholesky flop count | 2.3e+08 |

nnz(L+U), no partial pivoting, with AMD | 1,848,669 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 854,951 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 1,697,963 |

*Note that all matrix statistics (except nonzero pattern symmetry) exclude the 17760 explicit zero entries.
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SVD-based statistics: | |

norm(A) | 68743.4 |

min(svd(A)) | 0.000387463 |

cond(A) | 1.77419e+08 |

rank(A) | 5,489 |

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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