Matrix: Cylshell/s2rmt3m1

Description: FEM, cylindrical shell, 30x30 tri. mesh, stabilized MITC3 elements, R/t=100

Cylshell/s2rmt3m1 graph
(undirected graph drawing)

Cylshell/s2rmt3m1 graph

  • Home page of the UF Sparse Matrix Collection
  • Matrix group: Cylshell
  • Click here for a description of the Cylshell group.
  • Click here for a list of all matrices
  • Click here for a list of all matrix groups
  • download as a MATLAB mat-file, file size: 1 MB. Use UFget(1609) or UFget('Cylshell/s2rmt3m1') in MATLAB.
  • download in Matrix Market format, file size: 1 MB.
  • download in Rutherford/Boeing format, file size: 856 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 entries1,840
    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  s2rmt3m1.mtx                                                            
    %TITLE Cyl shell R/t=100 unif 30x30 trian mesh stab MITC3 elem with drill rot  
    %KEY   s2rmt3m1                                                                
    %CONTRIBUTOR Reijo Kouhia (                                
    %BEGIN DESCRIPTION                                                             
    % Matrix from a static analysis of a cylindrical shell                         
    % Radius to thickness ratio R/t = 100                                          
    % Length to radius ratio    R/L = 1                                            
    % One octant discretized with uniform 30 x 30 triangular 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 3-point 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 AMD544,292
    Cholesky flop count8.4e+07
    nnz(L+U), no partial pivoting, with AMD1,083,095
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD654,848
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD1,293,503

    Note that all matrix statistics (except nonzero pattern symmetry) exclude the 1840 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/s2rmt3m1 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.