Szczerba/Ill_Stokes
Ill-conditioned matrix from a Stokes problem, by Dominick Szczerba
| Name |
Ill_Stokes |
| Group |
Szczerba |
| Matrix ID |
1862 |
|
Num Rows
|
20,896 |
|
Num Cols
|
20,896 |
|
Nonzeros
|
191,368 |
|
Pattern Entries
|
191,368 |
|
Kind
|
Computational Fluid Dynamics Problem |
|
Symmetric
|
No |
|
Date
|
2007 |
|
Author
|
D. Szczerba |
|
Editor
|
T. Davis |
| Structural Rank |
20,896 |
| Structural Rank Full |
true |
|
Num Dmperm Blocks
|
1 |
|
Strongly Connect Components
|
1 |
|
Num Explicit Zeros
|
0 |
|
Pattern Symmetry
|
99% |
|
Numeric Symmetry
|
33% |
|
Cholesky Candidate
|
no |
|
Positive Definite
|
no |
|
Type
|
real |
| SVD Statistics |
| Matrix Norm |
5.442867e+00 |
| Minimum Singular Value |
2.415944e-09 |
| Condition Number |
2.252894e+09
|
| Rank |
20,896 |
| sprank(A)-rank(A) |
0 |
| Null Space Dimension |
0 |
| Full Numerical Rank? |
yes |
| Download Singular Values |
MATLAB
|
| Download |
MATLAB
Rutherford Boeing
Matrix Market
|
| Notes |
The matrix comes from a global formulation of the Stokes problem posed
directly (without pressure correction) on an unstructured tet mesh. It
includes momentum equations (3 quadrants) and continuity equation (last
quadrant). Unknowns are organized as : vx, vy, vz, p. The last quadrant
does not contain diagonal entries of course (continuity eq. does not
contain pressure) and is the reason bicgstab and related methods do not
work. Does not invert nicely with umfpack (strong oscillations in the
4th quadrant of the solution). LSQR produces better results (smaller
oscillations) but takes ages. Dominik Szczerba, Ph.D. Computer Vision
Lab, ETH. CH-8092 Zurich. http://www.vision.ee.ethz.ch/~domi
|
