Matrix: Sinclair/3Dspectralwave2

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

Sinclair/3Dspectralwave2 graph
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  • download as a MATLAB mat-file, file size: 73 MB. Use UFget(1857) or UFget('Sinclair/3Dspectralwave2') in MATLAB.
  • download in Matrix Market format, file size: 59 MB.
  • download in Rutherford/Boeing format, file size: 52 MB.

    Matrix properties
    number of rows292,008
    number of columns292,008
    structural full rank?yes
    structural rank292,008
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries1,387,472
    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 292008-by-1
    shiftsparse 292008-by-292008


    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 contains only one non-zero
    entry, representing a real y-directed source, placed approximately in the    
    centre.  The model size in elements is 10x10x10. 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 31 nodes. There are 3 unknown complex components at   
    each node - the x, y and z displacements. The A matrix therefore has         
    dimension 89373 x 89373.  ((10 x 4) - (10 - 1))^3 * 3 = 89373.  The solution 
    will consist of x-z planes.  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 AMD2,070,437,023
    Cholesky flop count4.2e+13
    nnz(L+U), no partial pivoting, with AMD4,140,582,038
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD3,742,233,527
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD7,912,859,348

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 1387472 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.