Matrix properties
number of rows	1,470,152
number of columns	1,470,152
nonzeros	84,422,970
structural full rank?	yes
structural rank	1,470,152
# of blocks from dmperm	39,045
# strongly connected comp.	39,045
explicit zero entries	2,666,022
nonzero pattern symmetry	symmetric
numeric value symmetry	symmetric
type	real
structure	symmetric
Cholesky candidate?	no
positive definite?	no

author	C. Janna, M. Ferronato
editor	T. Davis
date	2012
kind	structural problem
2D/3D problem?	yes

Notes:

Authors: Carlo Janna and Massimiliano Ferronato                        
Symmetric Indefinite Matrix                                            
# equations:   1,470,152                                               
# non-zeroes: 87,088,992                                               
Problem description: Coupled consolidation problem                     
                                                                       
The matrix Long_Coup is obtained from a 3D coupled consolidation       
problem of a geological formation discretized with tetrahedral Finite  
Elements. Due its complex geometry it was not possible to obtain a     
computational grid characterized by regularly shaped elements.  The    
copuled consolidation problem gives rise to a matrix having 4 unknowns 
associated to each node: the first three are displacement unknowns, the
fourth is a pressure. Coupled consolidation is a transient problem with
the matrix ill-conditioning strongly depending on the time step size.  
We provide a relatively simple problem, "dt0" with  a time step size of
10^0 seconds, and a more difficult one, "dt6" with a time step of 10^6 
seconds.  The two Long_Coup_* matrices are symmetric indefinite.       
Further information may be found in the following papers:              
                                                                       
1) C. Janna, M. Ferronato, G. Gambolati. "Parallel inexact constraint  
preconditioning for ill-conditioned consolidation problems".           
Computational Geosciences, submitted.                                  
                                                                       
2) M. Ferronato, L. Bergamaschi, G. Gambolati. "Performance and        
robustness of block constraint preconditioners in FE coupled           
consolidation problems".  International Journal for Numerical Methods  
in Engineering, 81, pp. 381-402, 2010.                                 
                                                                       
3) L. Bergamaschi, M. Ferronato, G. Gambolati. "Mixed constraint       
preconditioners for the iterative solution to FE coupled consolidation 
equations". Journal of Computational Physics, 227, pp. 9885-9897, 2008.
                                                                       
4) L. Bergamaschi, M. Ferronato, G. Gambolati. "Novel preconditioners  
for the iterative solution to FE-discretized coupled consolidation     
equations". Computer Methods in Applied Mechanics and Engineering, 196,
pp. 2647-2656, 2007.                                                   

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	14,265,014,032
Cholesky flop count	6.1e+14
nnz(L+U), no partial pivoting, with AMD	28,528,557,912
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	15,800,834,415
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	28,211,132,315

Note that all matrix statistics (except nonzero pattern symmetry) exclude the 2666022 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.