Matrix: Quaglino/viscoplastic1

Description: FEM discretization of a viscoplastic collision problem, Alessio Quaglino

Quaglino/viscoplastic1 graph Quaglino/viscoplastic1 graph
(bipartite graph drawing) (graph drawing of A+A')


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  • download as a MATLAB mat-file, file size: 3 MB. Use UFget(1868) or UFget('Quaglino/viscoplastic1') in MATLAB.
  • download in Matrix Market format, file size: 3 MB.
  • download in Rutherford/Boeing format, file size: 2 MB.

    Matrix properties
    number of rows4,326
    number of columns4,326
    structural full rank?yes
    structural rank4,326
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetry 74%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorA. Quaglino
    editorT. Davis
    kindmaterials problem
    2D/3D problem?yes

    Additional fieldssize and type
    bfull 4326-by-1
    Ccell 7-by-1


    The matrix is in the form [A11 A12 ; A21 A22] where A11 and A22 are diagonal. 
    Originally, the matrices in this set were poorly scaled, but this was resolved
    by a scale factor of the form [A11 A12*e ; A21/e A4] where the scalar e is    
    of magnitude 1e2 but can be 1e6 or 1e7 for a stiff material.  The Problem.A   
    matrix is the properly scaled problem.  The Problem.aux.C{1:7} matrices have  
    been "unscaled" with a factor e = 10.^(-(1:7)), to give a sequence of matrices
    that are well scaled to poorly scaled, and thus well conditioned (C{1}) to    
    poorly conditioned (C{7}).  This mimics the original poorly scaled and ill-   
    conditioned problem, and may be of interest for those developing algorithms   
    for automatic scaling.  From a FEM discretization of a viscoplastic collision 
    problem, Alessio Quaglino.                                                    

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD71,771
    Cholesky flop count2.2e+06
    nnz(L+U), no partial pivoting, with AMD139,216
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD705,015
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD1,530,390

    SVD-based statistics:
    null space dimension0
    full numerical rank?yes

    singular values (MAT file):click here
    SVD method used:s = piro_band_svd (A)

    Quaglino/viscoplastic1 svd

    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.