Matrix: Janna/CoupCons3D

Description: 3D fully coupled poroelastic problem

Janna/CoupCons3D graph
(undirected graph drawing)


Janna/CoupCons3D dmperm of Janna/CoupCons3D

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  • Matrix group: Janna
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  • download as a MATLAB mat-file, file size: 135 MB. Use UFget(2647) or UFget('Janna/CoupCons3D') in MATLAB.
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    Matrix properties
    number of rows416,800
    number of columns416,800
    nonzeros17,277,420
    structural full rank?yes
    structural rank416,800
    # of blocks from dmperm84,321
    # strongly connected comp.84,321
    explicit zero entries5,044,916
    nonzero pattern symmetrysymmetric
    numeric value symmetry 1%
    typereal
    structureunsymmetric
    Cholesky candidate?no
    positive definite?no

    authorC. Janna, M. Ferronato, G. Pini
    editorT. Davis
    date2012
    kindstructural problem
    2D/3D problem?yes

    Notes:

    Authors: Carlo Janna, Massimiliano Ferronato Giorgio Pini       
    Matrix type: Unsymmetric                                        
    # equations:      416,800                                       
    # non-zeroes:   22,322,336                                      
                                                                    
    Problem description: Fully coupled poroelastic problem          
    (structural problem)                                            
                                                                    
                                                                    
    The matrix CoupCons3D has been obtained through a Finite Element
    transient simulation of a fully coupled consolidation problem on
    a three-dimensional domain using Finite Differences for the     
    discretization in time.                                         
                                                                    
    Further information can be found in the following papers:       
                                                                    
    1) M. Ferronato, G. Pini, and G. Gambolati. The role of         
    preconditioning in the solution to FE coupled consolidation     
    equations by Krylov subspace methods.  International Journal for
    Numerical and Analytical Methods in Geomechanics 33 (2009), pp. 
    405-423.                                                        
                                                                    
    2) M. Ferronato, C. Janna, and G. Pini. Parallel solution to    
    ill-conditioned FE geomechanical problems. International Journal
    for Numerical and Analytical Methods in Geomechanics 36 (2012), 
    pp. 422-437.                                                    
                                                                    
    3) 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 AMD255,454,187
    Cholesky flop count7.1e+11
    nnz(L+U), no partial pivoting, with AMD510,491,574
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD382,662,721
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD716,433,504

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 5044916 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.