Matrix properties
number of rows	638,802
number of columns	638,802
nonzeros	27,245,944
structural full rank?	yes
structural rank	638,802
# of blocks from dmperm	21,880
# strongly connected comp.	21,880
explicit zero entries	1,368,620
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:  638802                                            
# non-zeroes: 28614564                                          
Problem description: contact mechanics                          
                                                                
The matrix Fault_639 is obtained from a structural problem      
discretizing a faulted gas reservoir with tetrahedral Finite    
Elements and triangular Interface Elements.  The Interface      
Elements are used with a Penalty formulation to simulate the    
faults behaviour.  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. "Numerical 
modelling of regional faults in land subsidence prediction above
gas/oil reservoirs", International Journal for Numerical and    
Analytical Methods in Geomechanics, 32, pp. 633-657, 2008.      
                                                                
2) M. Ferronato, C. Janna, G. Gambolati. "Mixed constraint      
preconditioning in computational contact mechanics", Computer   
Methods in Applied Mechanics and Engineering, 197, pp.          
3922-3931, 2008.                                                
                                                                
3) C. Janna, M. Ferronato, G. Gambolati. "Multilevel incomplete 
factorizations for the iterative solution of non-linear FE      
problems". International Journal for Numerical Methods in       
Engineering, 80, pp. 651-670, 2009.                             
                                                                
4) 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	3,179,862,040
Cholesky flop count	6.4e+13
nnz(L+U), no partial pivoting, with AMD	6,359,085,278
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	3,950,893,717
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	6,902,951,841

Note that all matrix statistics (except nonzero pattern symmetry) exclude the 1368620 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.