Matrix: Janna/Fault_639

Description: contact mechanics for model of a faulted gas reservoir

Janna/Fault_639 graph
(undirected graph drawing)

Janna/Fault_639 dmperm of Janna/Fault_639

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  • download as a MATLAB mat-file, file size: 163 MB. Use UFget(2543) or UFget('Janna/Fault_639') in MATLAB.
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    Matrix properties
    number of rows638,802
    number of columns638,802
    structural full rank?yes
    structural rank638,802
    # of blocks from dmperm21,880
    # strongly connected comp.21,880
    explicit zero entries1,368,620
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?yes

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


    Authors: Carlo Janna and Massimiliano Ferronato                 
    Symmetric Positive Definite Matrix                              
    # equations:  638802                                            
    # non-zeroes: 28614564                                          
    Problem description: contact mechanics                          
    The matrix Fault_639 is obtained from a structural problem      
    discretizing a faulted gas reservoir with tetrahedral Finite    
    Elements and triangular Interface Elements.  The Interface      
    Elements are used with a Penalty formulation to simulate the    
    faults behaviour.  The problem arises from a 3D discretization  
    with three displacement unknowns associated to each node of the 
    grid.  Some further information may be found in the following   
    1) M. Ferronato, G. Gambolati, C. Janna, P. Teatini. "Numerical 
    modelling of regional faults in land subsidence prediction above
    gas/oil reservoirs", International Journal for Numerical and    
    Analytical Methods in Geomechanics, 32, pp. 633-657, 2008.      
    2) M. Ferronato, C. Janna, G. Gambolati. "Mixed constraint      
    preconditioning in computational contact mechanics", Computer   
    Methods in Applied Mechanics and Engineering, 197, pp.          
    3922-3931, 2008.                                                
    3) C. Janna, M. Ferronato, G. Gambolati. "Multilevel incomplete 
    factorizations for the iterative solution of non-linear FE      
    problems". International Journal for Numerical Methods in       
    Engineering, 80, pp. 651-670, 2009.                             
    4) C. Janna, M. Ferronato, G. Gambolati. "A Block FSAI-ILU      
    parallel preconditioner for symmetric positive definite linear  
    systems". SIAM Journal on Scientific Computing, 32, pp.         
    2468-2484, 2010.                                                

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD3,179,862,040
    Cholesky flop count6.4e+13
    nnz(L+U), no partial pivoting, with AMD6,359,085,278
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD3,950,893,717
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD6,902,951,841

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 1368620 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.