3D coupled consolidation problem (geological formation)
Name Long_Coup_dt6
Group Janna
Matrix ID 2551
Num Rows 1,470,152
Num Cols 1,470,152
Nonzeros 84,422,970
Pattern Entries 87,088,992
Kind Structural Problem
Symmetric Yes
Date 2012
Author C. Janna, M. Ferronato
Editor T. Davis
Structural Rank 1,470,152
Structural Rank Full true
Num Dmperm Blocks 39,045
Strongly Connect Components 39,045
Num Explicit Zeros 2,666,022
Pattern Symmetry 100%
Numeric Symmetry 100%
Cholesky Candidate no
Positive Definite no
Type real
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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.