Matrix: Janna/Cube_Coup_dt0

Description: 3D coupled consolidation problem (3D cube)

Janna/Cube_Coup_dt0 graph
(undirected graph drawing)

Janna/Cube_Coup_dt0 dmperm of Janna/Cube_Coup_dt0

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  • download as a MATLAB mat-file, file size: 542 MB. Use UFget(2548) or UFget('Janna/Cube_Coup_dt0') in MATLAB.
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    Matrix properties
    number of rows2,164,760
    number of columns2,164,760
    structural full rank?yes
    structural rank2,164,760
    # of blocks from dmperm47,061
    # strongly connected comp.47,061
    explicit zero entries2,800,074
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?no
    positive definite?no

    authorC. Janna, M. Ferronato
    editorT. Davis
    kindstructural problem
    2D/3D problem?yes


    Authors: Carlo Janna and Massimiliano Ferronato                        
    Symmetric Indefinite Matrix                                            
    # equations:    2,164,760                                              
    # non-zeroes: 127,206,144                                              
    Problem description: Coupled consolidation problem                     
    The matrix Cube_Coup is obtained from a 3D coupled consolidation       
    problem of a cube discretized with tetrahedral Finite Elements. The    
    computational grid is characterized by regularly shaped elements.  The 
    copuled consolidation problem gives rise to a matrix having 4 unknowns 
    associated to each node: the first three are displacement unknowns, the
    fourth is a pressure. Coupled consolidation is a transient problem with
    the matrix ill-conditioning strongly depending on the time step size.  
    We provide a relatively simple problem, "dt0" with  a time step size of
    10^0 seconds, and a more difficult one, "dt6" with a time step of 10^6 
    seconds.  The two Cube_Coup_* matrices are symmetric indefinite.       
    Further information may be found in the following papers:              
    1) C. Janna, M. Ferronato, G. Gambolati. "Parallel inexact constraint  
    preconditioning for ill-conditioned consolidation problems".           
    Computational Geosciences, submitted.                                  
    2) M. Ferronato, L. Bergamaschi, G. Gambolati. "Performance and        
    robustness of block constraint preconditioners in FE coupled           
    consolidation problems".  International Journal for Numerical Methods  
    in Engineering, 81, pp. 381-402, 2010.                                 
    3) L. Bergamaschi, M. Ferronato, G. Gambolati. "Mixed constraint       
    preconditioners for the iterative solution to FE coupled consolidation 
    equations". Journal of Computational Physics, 227, pp. 9885-9897, 2008.
    4) L. Bergamaschi, M. Ferronato, G. Gambolati. "Novel preconditioners  
    for the iterative solution to FE-discretized coupled consolidation     
    equations". Computer Methods in Applied Mechanics and Engineering, 196,
    pp. 2647-2656, 2007.                                                   

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD23,050,250,222
    Cholesky flop count1.1e+15
    nnz(L+U), no partial pivoting, with AMD46,098,335,684
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD26,187,685,977
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD46,514,870,558

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 2800074 explicit zero entries.

    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.