Matrix: Janna/Flan_1565

Description: 3D model of a steel flange, hexahedral finite elements

Janna/Flan_1565 graph
(undirected graph drawing)


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  • download as a MATLAB mat-file, file size: 286 MB. Use UFget(2544) or UFget('Janna/Flan_1565') in MATLAB.
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    Matrix properties
    number of rows1,564,794
    number of columns1,564,794
    structural full rank?yes
    structural rank1,564,794
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries3,240,672
    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:    1564794                                         
    # non-zeroes: 117406044                                         
    Problem description: Structural problem                         
    The matrix Flan_1565 is obtained from a 3D mechanical problem   
    discretizing a steel flange with hexahedral Finite Elements. Due
    to the regular shape of the mechanical piece, the computational 
    grid is a structured mesh with regularly shaped elements. Three 
    displacement unknowns are associated to each node of the grid.  
    Some further information may be found in the following papers:  
    1) C. Janna, A. Comerlati, G. Gambolati. "A comparison of       
    projective and direct solvers for finite elements in            
    elastostatics". Advances in Engineering Software, 40, pp.       
    675-685, 2009.                                                  
    2) 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 AMD3,651,940,140
    Cholesky flop count2.2e+13
    nnz(L+U), no partial pivoting, with AMD7,302,315,486
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD6,488,489,176
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD12,183,623,118

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 3240672 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.