Matrix properties
number of rows	923,136
number of columns	923,136
nonzeros	40,373,538
structural full rank?	yes
structural rank	923,136
# of blocks from dmperm	14,425
# strongly connected comp.	14,425
explicit zero entries	631,668
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:  923136                                            
# non-zeroes: 41005206                                          
Problem description: Geomechanical problem                      
                                                                
The matrix Emilia_923 is obtained from a structural problem     
discretizing a gas reservoir with tetrahedral Finite Elements.  
Due to the complex geometry of the geological formation it was  
not possible to obtain a computational grid characterized by    
regularly shaped elements.  The problem arises from a 3D        
discretization with three displacement unknowns associated to   
each node of the grid.  Some further information may be found in
the following papers:                                           
                                                                
1) M. Ferronato, G. Gambolati, C. Janna, P. Teatini.            
"Geomechanical issues of anthropogenic CO2 sequestration in     
exploited gas fields", Energy Conversion and Management, 51, pp.
1918-1928, 2010.                                                
                                                                
2) C. Janna, M. Ferronato. "Adaptive pattern research for block 
FSAI preconditionig". SIAM Journal on Scientific Computing, to  
appear.                                                         

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	5,317,434,978
Cholesky flop count	1.3e+14
nnz(L+U), no partial pivoting, with AMD	10,633,946,820
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	6,960,196,599
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	12,298,145,622

Note that all matrix statistics (except nonzero pattern symmetry) exclude the 631668 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.