Matrix: Szczerba/Ill_Stokes

Description: Ill-conditioned matrix from a Stokes problem, by Dominick Szczerba

Szczerba/Ill_Stokes graph Szczerba/Ill_Stokes graph
(bipartite graph drawing) (graph drawing of A+A')


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  • download as a MATLAB mat-file, file size: 2 MB. Use UFget(1862) or UFget('Szczerba/Ill_Stokes') in MATLAB.
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    Matrix properties
    number of rows20,896
    number of columns20,896
    structural full rank?yes
    structural rank20,896
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetry 99%
    numeric value symmetry 33%
    Cholesky candidate?no
    positive definite?no

    authorD. Szczerba
    editorT. Davis
    kindcomputational fluid dynamics problem
    2D/3D problem?yes

    Additional fieldssize and type
    bfull 20896-by-1


    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.            

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD3,280,425
    Cholesky flop count2.1e+09
    nnz(L+U), no partial pivoting, with AMD6,539,954
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD7,800,780
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD13,814,174

    SVD-based statistics:
    null space dimension0
    full numerical rank?yes

    singular values (MAT file):click here
    SVD method used:s = svd (full (R)) ; where [~,R,E] = spqr (A) with droptol of zero

    Szczerba/Ill_Stokes svd

    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.