Matrix properties
number of rows	742,793
number of columns	742,793
nonzeros	37,138,461
structural full rank?	yes
structural rank	742,793
# of blocks from dmperm	57,652
# strongly connected comp.	57,652
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	2014
kind	2D/3D problem
2D/3D problem?	yes

Notes:

Janna/PFlow_742: 3D pressure-temperature evolution in porous media
                                                                  
Authors: Carlo Janna and Massimiliano Ferronato                   
Symmetric Positive Definite Matrix                                
# equations:     742,793                                          
# non-zeroes: 37,138,461                                          
                                                                  
The matrix PFlow_742 is obtained from a 3D simulation of the      
pressure-temperature field in a multilayered porous media         
discretized by hexahedral Finite Elements. The ill-conditioning   
of the matrix is due to the strong contrasts in the material      
properties fo different layers.                                   
                                                                  
Further information may be found in the following paper:          
                                                                  
1) C. Janna, M. Ferronato, G. Gambolati. "The use of supernodes   
in factored sparse approximate inverse preconditioning". SIAM     
Journal on Scientific Computing, submitted.                       

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	1,124,528,164
Cholesky flop count	5.4e+12
nnz(L+U), no partial pivoting, with AMD	2,248,313,535
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	1,851,385,449
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	4,000,348,915

For a description of the statistics displayed above, click here.

Maintained by Tim Davis, last updated 10-Jun-2015.
Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.