Matrix properties
number of rows	90,449
number of columns	90,449
nonzeros	4,427,725
structural full rank?	yes
structural rank	90,449
# of blocks from dmperm	1
# strongly connected comp.	1
explicit zero entries	393,166
nonzero pattern symmetry	symmetric
numeric value symmetry	symmetric
type	real
structure	symmetric
Cholesky candidate?	yes
positive definite?	yes

author	R. Kouhia
editor	R. Boisvert, R. Pozo, K. Remington, B. Miller, R. Lipman, R. Barrett, J. Dongarra
date	1997
kind	structural problem
2D/3D problem?	yes

Additional fields	size and type
coord	full 90449-by-3

Notes:

%                                                                              
%FILE  s3dkq4m2.mtx                                                            
%TITLE Cyl shell R/t=1000 unif 150x100 quad mesh DKQ elem with drill rot       
%KEY   s3dkq4m2                                                                
%                                                                              
%                                                                              
%CONTRIBUTOR Reijo Kouhia (reijo.kouhia@hut.fi)                                
%                                                                              
%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 = 1000                                         
% Length to radius ratio    R/L = 1                                            
% One octant discretized with uniform 150 x 100 quadrilateral mesh             
% element:                                                                     
% facet-type shell element where the bending part is formulated                
% using the discrete Kirchhoff quadrilateral (Lyons-Crisfield version),        
% 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 AMD	27,399,094
Cholesky flop count	1.8e+10
nnz(L+U), no partial pivoting, with AMD	54,707,739
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	50,277,848
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	98,614,571

Note that all matrix statistics (except nonzero pattern symmetry) exclude the 393166 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.