Matrix: Cylshell/s1rmq4m1

Description: FEM, cylindrical shell, 30x30 quad. mesh, stabilized MITC4 elements, R/t=10

Cylshell/s1rmq4m1 graph
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Cylshell/s1rmq4m1 graph

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  • Matrix group: Cylshell
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  • download as a MATLAB mat-file, file size: 1 MB. Use UFget(1605) or UFget('Cylshell/s1rmq4m1') in MATLAB.
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  • download in Rutherford/Boeing format, file size: 831 KB.

    Matrix properties
    number of rows5,489
    number of columns5,489
    structural full rank?yes
    structural rank5,489
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries18,700
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?yes

    authorR. Kouhia
    editorR. Boisvert, R. Pozo, K. Remington, B. Miller, R. Lipman, R. Barrett, J. Dongarra
    kindstructural problem
    2D/3D problem?yes

    Additional fieldssize and type
    coordfull 5489-by-3


    %FILE  s1rmq4m1.mtx                                                            
    %TITLE Cyl shell R/t = 10 unif 30x30 quad mesh stab MITC4 elem with drill rot  
    %KEY   s1rmq4m1                                                                
    %CONTRIBUTOR Reijo Kouhia (                                
    %REFERENCE   M. Benzi, R. Kouhia, M.Tuma: An assesment of some                 
    %            preconditioning techniques in shell problems                      
    %            Technical Report LA-UR-97-3892, Los Alamos National Laboratory    
    %BEGIN DESCRIPTION                                                             
    % Matrix from a static analysis of a cylindrical shell                         
    % Radius to thickness ratio R/t = 10                                           
    % Length to radius ratio    R/L = 1                                            
    % One octant discretized with uniform 30 x 30 quadrilateral mesh               
    % element:                                                                     
    % facet-type shell element where the bending part is formulated                
    % using the stabilized MITC theory (stabilization paramater 0.4)               
    % the membrane part includes drilling rotations using                          
    % the Hughes-Brezzi formulation with (regularizing parameter = G/1000,         
    % where G is the shear modulus)                                                
    % full 2x2 Gauss-Legendre integration                                          
    % --------------------------------------------------------------------------   
    % Note:                                                                        
    % The sparsity pattern of the matrix is determined from the element            
    % connectivity data assuming that the element matrix is full.                  
    % Since this case the  material model is linear isotropically elastic          
    % and the FE mesh is  uniform there exist some zeros.                          
    % Since the removal of those zero elements is trivial                          
    % but the reconstruction of the current sparsity                               
    % pattern is impossible from the sparsified structure without any further      
    % knowledge of the element connectivity, the zeros are retained in this file.  
    % ---------------------------------------------------------------------------  
    %END DESCRIPTION                                                               

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD846,206
    Cholesky flop count1.9e+08
    nnz(L+U), no partial pivoting, with AMD1,686,923
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD875,290
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD1,735,331

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 18700 explicit zero entries.

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

    singular values (MAT file):click here
    SVD method used:s = svd (full (A)) ;

    Cylshell/s1rmq4m1 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.