Janna/Long_Coup_dt0
3D coupled consolidation problem (geological formation)
Name 
Long_Coup_dt0 
Group 
Janna 
Matrix ID 
2550 
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 
Download 
MATLAB
Rutherford Boeing
Matrix Market

Notes 
Authors: Carlo Janna and Massimiliano Ferronato
Symmetric Indefinite Matrix
# equations: 1,470,152
# nonzeroes: 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 illconditioning 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 illconditioned 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. 381402, 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. 98859897, 2008.
4) L. Bergamaschi, M. Ferronato, G. Gambolati. "Novel preconditioners
for the iterative solution to FEdiscretized coupled consolidation
equations". Computer Methods in Applied Mechanics and Engineering, 196,
pp. 26472656, 2007.
