Matrix: Sinclair/3Dspectralwave

Description: 3-D spectral-element elastic wave modelling in freq. domain, C. Sinclair, Univ. Adelaide

Sinclair/3Dspectralwave graph
(undirected graph drawing)


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  • Matrix group: Sinclair
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  • download as a MATLAB mat-file, file size: 150 MB. Use UFget(1856) or UFget('Sinclair/3Dspectralwave') in MATLAB.
  • download in Matrix Market format, file size: 125 MB.
  • download in Rutherford/Boeing format, file size: 105 MB.

    Matrix properties
    number of rows680,943
    number of columns680,943
    structural full rank?yes
    structural rank680,943
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries3,359,762
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?no

    authorC. Sinclair
    editorT. Davis
    kindmaterials problem
    2D/3D problem?yes

    Additional fieldssize and type
    bsparse 680943-by-1
    shiftsparse 680943-by-680943


    The A matrix is produced using 3-D spectral-element elastic wave modelling in
    the frequency domain. The medium is homogeneous and isotropic with elastic   
    coefficients: c11 = 6.30,  c44 = 1.00 The B matrix represents a real         
    y-directed source, placed approximately in the centre.  The model size in    
    elements is 20x20x20. Each element is 1m x1m x 1m. Each element is a 4x4x4   
    Gauss-Lobbato-Legendre mesh, so the height, width and depth of the system is 
    61 nodes. There are 3 unknown components at each node - the x, y and z       
    displacements. The A matrix therefore has dimension 680943 x 680943, where   
    ((20 x 4) - (20 - 1))^3 * 3 = 680943. The problem domain is earth sciences.  
    Note that A is complex and b is sparse and real (b has a single nonzero).    
    The A matrix was provided with a nonzero imaginary part, but was otherwise   
    complex Hermitian.  To save space in the Matrix Market and Rutherford/Boeing 
    formats, the A matrix here has had this imaginary diagonal removed.  The     
    shift can be found in the aux.shift auxiliary matrix.  To reproduce the      
    original A matrix, use A = Problem.A + Problem.aux.shift ;                   

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD9,565,680,684
    Cholesky flop count4.3e+14
    nnz(L+U), no partial pivoting, with AMD19,130,680,425
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD16,486,249,140
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD34,447,602,838

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 3359762 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.