Matrix: Janna/Geo_1438

Description: geomechanical model of earth crust with underground deformation

Janna/Geo_1438 graph
(undirected graph drawing)

Janna/Geo_1438 dmperm of Janna/Geo_1438

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  • Matrix group: Janna
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  • download as a MATLAB mat-file, file size: 354 MB. Use UFget(2545) or UFget('Janna/Geo_1438') in MATLAB.
  • download in Matrix Market format, file size: 280 MB.
  • download in Rutherford/Boeing format, file size: 229 MB.

    Matrix properties
    number of rows1,437,960
    number of columns1,437,960
    structural full rank?yes
    structural rank1,437,960
    # of blocks from dmperm66,481
    # strongly connected comp.66,481
    explicit zero entries2,920,368
    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:   1437960                                          
    # non-zeroes: 63156690                                          
    Problem description: Geomechanical problem                      
    The matrix Geo_1438 is obtained from a geomechanical problem    
    discretizing a region of the earth crust subject to underground 
    deformation. The computational domain is a box with an areal    
    extent of 50 x 50 km and 10 km deep consisting of regularly     
    shaped tetrahedral Finite Elements.  The problem arises from a  
    3D discretization with three displacement unknowns associated to
    each node of the grid.  This matrix has been used as a test case
    in the following paper:                                         
    1) 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 AMD6,297,700,169
    Cholesky flop count1.2e+14
    nnz(L+U), no partial pivoting, with AMD12,593,962,378
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD7,633,969,695
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD13,733,310,294

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 2920368 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.