Janna/Cube_Coup_dt6
3D coupled consolidation problem (3D cube)
Name 
Cube_Coup_dt6 
Group 
Janna 
Matrix ID 
2549 
Num Rows

2,164,760 
Num Cols

2,164,760 
Nonzeros

124,406,070 
Pattern Entries

127,206,144 
Kind

Structural Problem 
Symmetric

Yes 
Date

2012 
Author

C. Janna, M. Ferronato 
Editor

T. Davis 
Structural Rank 
2,164,760 
Structural Rank Full 
true 
Num Dmperm Blocks

47,061 
Strongly Connect Components

47,061 
Num Explicit Zeros

2,800,074 
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: 2,164,760
# nonzeroes: 127,206,144
Problem description: Coupled consolidation problem
The matrix Cube_Coup is obtained from a 3D coupled consolidation
problem of a cube discretized with tetrahedral Finite Elements. The
computational grid is 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 Cube_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.
