Matrix: Janna/Queen_4147

Description: 3D structural problem

Janna/Queen_4147 graph
(undirected graph drawing)


Janna/Queen_4147 dmperm of Janna/Queen_4147

  • 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: 1933 MB. Use UFget(2660) or UFget('Janna/Queen_4147') in MATLAB.
  • download in Matrix Market format, file size: 1480 MB.
  • download in Rutherford/Boeing format, file size: 1181 MB.

    Matrix properties
    number of rows4,147,110
    number of columns4,147,110
    nonzeros316,548,962
    structural full rank?yes
    structural rank4,147,110
    # of blocks from dmperm149,447
    # strongly connected comp.149,447
    explicit zero entries12,950,322
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typereal
    structuresymmetric
    Cholesky candidate?yes
    positive definite?yes

    authorC. Janna, M. Ferronato
    editorT. Davis
    date2014
    kind2D/3D problem
    2D/3D problem?yes

    Notes:

    Janna/Queen_4147: 3D structural problem                        
                                                                   
    Authors: Carlo Janna and Massimiliano Ferronato                
    Symmetric Positive Definite Matrix                             
    # equations:     4,147,110                                     
    # non-zeroes:  329,499,288                                     
                                                                   
    The matrix Queen_4147 is obtained from the 3D discretizaion    
    of a structural problem by isoparametric hexahedral Finite     
    Elements. The solid material is strongly heterogeneous and     
    several elements exhibit shape distortion thus producing an    
    ill-conditioned stiffness matrix.                              
                                                                   
    Further information may be found in the following paper:       
                                                                   
    1) C. Janna, M. Ferronato, G. Gambolati. "The use of supernodes
    in factored sparse approximate inverse preconditioning". SIAM  
    Journal on Scientific Computing, submitted.                    
    

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD64,402,387,996
    Cholesky flop count4.9e+15
    nnz(L+U), no partial pivoting, with AMD128,800,628,882
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD70,146,293,583
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD123,868,718,534

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 12950322 explicit zero entries.

    For a description of the statistics displayed above, click here.

    Maintained by Tim Davis, last updated 04-Jun-2015.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.