Matrix properties
number of rows	1,465,137
number of columns	1,465,137
nonzeros	21,005,389
structural full rank?	yes
structural rank	1,465,137
# of blocks from dmperm	29,105
# strongly connected comp.	29,105
explicit zero entries	0
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	computational fluid dynamics problem
2D/3D problem?	yes

Notes:

Authors: Carlo Janna and Massimiliano Ferronato                 
                                                                
Symmetric Positive Definite Matrix                              
# equations:   1465137                                          
# non-zeroes: 21005389                                          
Problem description: Flow in porous medium with stochastic      
permeabilies                                                    
                                                                
The matrix StocF_1465 is obtained from a fluid-dynamical problem
of flow in porous medium.  The computational grid consists of   
tetrahedral Finite Elements discretizing an underground aquifer 
with stochastic permeabilties.  Some further information may be 
found in the following papers:                                  
                                                                
1) C. Janna, M. Ferronato. "Adaptive pattern research for Block 
FSAI preconditioning".  SIAM Journal on Scientific Computing, to
appear.                                                         
                                                                
2) M. Ferronato, C. Janna, G. Pini. "Shifted FSAI               
preconditioners for the efficient parallel solution of          
non-linear groundwater flow models". International Journal for  
Numerical Methods in Engineering, to appear.                    

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	3,846,080,925
Cholesky flop count	4.3e+13
nnz(L+U), no partial pivoting, with AMD	7,690,696,713
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	5,963,770,110
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	10,536,150,363

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.