| 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 |
| entries not in dmperm blocks | 0 |
| 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 |
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: | AMD | METIS |
| nnz(chol(P*(A+A'+s*I)*P')) | 27,399,094 | 17,968,333 |
| Cholesky flop count | 1.8e+10 | 7.2e+09 |
| nnz(L+U), no partial pivoting | 54,707,739 | 35,846,217 |
| nnz(V) for QR, upper bound nnz(L) for LU | 50,277,848 | 28,925,303 |
| nnz(R) for QR, upper bound nnz(U) for LU | 98,614,571 | 54,790,898 |
Note that all matrix statistics (except nonzero pattern symmetry) exclude the 393166 explicit zero entries.
Maintained by Tim Davis, last updated 04-May-2008.
Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.