Matrix: Janna/ML_Laplace

Description: 2D Poisson problem, meshless local Petrov-Galerkin method

Janna/ML_Laplace graph
(undirected graph drawing)

Janna/ML_Laplace dmperm of Janna/ML_Laplace

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  • download as a MATLAB mat-file, file size: 192 MB. Use UFget(2648) or UFget('Janna/ML_Laplace') in MATLAB.
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    Matrix properties
    number of rows377,002
    number of columns377,002
    structural full rank?yes
    structural rank377,002
    # of blocks from dmperm2,503
    # strongly connected comp.2,503
    explicit zero entries107,274
    nonzero pattern symmetrysymmetric
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

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


    Authors: Carlo Janna, Massimiliano Ferronato, Giorgio Pini       
    Matrix type: Unsymmetric                                         
    # equations:       377,002                                       
    # non-zeroes:   27,689,972                                       
    Problem description: Poisson problem                             
    The matrix ML_Laplace has been obtained by discretizing a 2D     
    Poisson equation with a Meshless Local Petrov-Galerkin method.   
    Further information can be found in the following papers:        
    1) G. Pini, A. Mazzia, and F. Sartoretto. Accurate MLPG solution 
    of 3D potential problems. CMES - Computer Modeling in Engineering
    & Sciences 36 (2008), pp. 43-64.                                 
    2) M. Ferronato, C. Janna and G. Pini. A generalized Block FSAI  
    preconditioner for unsymmetric indefinite matrices. Journal of   
    Computational and Applied Mathematics (2012), submitted.         

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD284,522,480
    Cholesky flop count5.0e+11
    nnz(L+U), no partial pivoting, with AMD568,667,958
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD455,980,664
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD899,086,831

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 107274 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.