Matrix: Janna/Long_Coup_dt6

Description: 3D coupled consolidation problem (geological formation)

Janna/Long_Coup_dt6 graph
(undirected graph drawing)

Janna/Long_Coup_dt6 dmperm of Janna/Long_Coup_dt6

  • Home page of the UF Sparse Matrix Collection
  • Matrix group: Janna
  • Click here for a description of the Janna group.
  • Click here for a list of all matrices
  • Click here for a list of all matrix groups
  • download as a MATLAB mat-file, file size: 481 MB. Use UFget(2551) or UFget('Janna/Long_Coup_dt6') in MATLAB.
  • download in Matrix Market format, file size: 339 MB.
  • download in Rutherford/Boeing format, file size: 272 MB.

    Matrix properties
    number of rows1,470,152
    number of columns1,470,152
    structural full rank?yes
    structural rank1,470,152
    # of blocks from dmperm39,045
    # strongly connected comp.39,045
    explicit zero entries2,666,022
    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:   1,470,152                                               
    # non-zeroes: 87,088,992                                               
    Problem description: Coupled consolidation problem                     
    The matrix Long_Coup is obtained from a 3D coupled consolidation       
    problem of a geological formation discretized with tetrahedral Finite  
    Elements. Due its complex geometry it was not possible to obtain a     
    computational grid 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 Long_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 AMD14,265,014,032
    Cholesky flop count6.1e+14
    nnz(L+U), no partial pivoting, with AMD28,528,557,912
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD15,800,834,415
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD28,211,132,315

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 2666022 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.