Matrix properties
number of rows	1,564,794
number of columns	1,564,794
nonzeros	114,165,372
structural full rank?	yes
structural rank	1,564,794
# of blocks from dmperm	1
# strongly connected comp.	1
explicit zero entries	3,240,672
nonzero pattern symmetry	symmetric
numeric value symmetry	symmetric
type	real
structure	symmetric
Cholesky candidate?	yes
positive definite?	yes

author	C. Janna, M. Ferronato
editor	T. Davis
date	2011
kind	structural problem
2D/3D problem?	yes

Notes:

Authors: Carlo Janna and Massimiliano Ferronato                 
                                                                
Symmetric Positive Definite Matrix                              
# equations:    1564794                                         
# non-zeroes: 117406044                                         
Problem description: Structural problem                         
                                                                
The matrix Flan_1565 is obtained from a 3D mechanical problem   
discretizing a steel flange with hexahedral Finite Elements. Due
to the regular shape of the mechanical piece, the computational 
grid is a structured mesh with regularly shaped elements. Three 
displacement unknowns are associated to each node of the grid.  
Some further information may be found in the following papers:  
                                                                
1) C. Janna, A. Comerlati, G. Gambolati. "A comparison of       
projective and direct solvers for finite elements in            
elastostatics". Advances in Engineering Software, 40, pp.       
675-685, 2009.                                                  
                                                                
2) C. Janna, M. Ferronato, G. Gambolati. "A Block FSAI-ILU      
parallel preconditioner for symmetric positive definite linear  
systems". SIAM Journal on Scientific Computing, 32, pp.         
2468-2484, 2010.                                                

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	3,651,940,140
Cholesky flop count	2.2e+13
nnz(L+U), no partial pivoting, with AMD	7,302,315,486
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	6,488,489,176
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	12,183,623,118

Note that all matrix statistics (except nonzero pattern symmetry) exclude the 3240672 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.