Finite element simulations: gas reservoir and structural problems. Univ Padova.
C. Janna, Univ. of Padova. Authors: Carlo Janna and Massimiliano Ferronato
All matrices in the set are symmetric and positive definite.
Serena:
Gas reservoir simulation for CO2 sequestration.
# equations: 1,391,349
# non-zeroes: 64,531,701
Problem description: structural problem
The matrix Serena is obtained from a structural problem discretizing a gas
reservoir with tetrahedral Finite Elements. The medium is strongly
heterogeneous and characterized by a complex geometry consisting of
alternating sequences of thin clay and sand layers. References: [1]
Emilia_923:
# equations: 923136
# non-zeroes: 41005206
Problem description: Geomechanical problem
The matrix Emilia_923 is obtained from a structural problem discretizing a
gas reservoir with tetrahedral Finite Elements. Due to the complex
geometry of the geological formation it was not possible to obtain a
computational grid characterized by regularly shaped elements. The
problem arises from a 3D discretization with three displacement unknowns
associated to each node of the grid. References: [1], [2]
Fault_639:
# 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. References [3,4,5,6]
Flan_1565:
# equations: 1564794
# non-zeroes: 117406044
Problem description: Structural problem
The matrix Flan_1565 is obtained from a 3D mechanical problem discretizing
a steel flange with hexahedral Finite Elements. Due to the regular shape
of the mechanical piece, the computational grid is a structured mesh with
regularly shaped elements. Three displacement unknowns are associated to
each node of the grid. References [6,7]
Geo_1438:
# equations: 1437960
# non-zeroes: 63156690
Problem description: Geomechanical problem
The matrix Geo_1438 is obtained from a geomechanical problem discretizing
a region of the earth crust subject to underground deformation. The
computational domain is a box with an areal extent of 50 x 50 km and 10 km
deep consisting of regularly shaped tetrahedral Finite Elements. The
problem arises from a 3D discretization with three displacement unknowns
associated to each node of the grid. Reference: [6]
Hook_1498:
# equations: 1498023
# non-zeroes: 60917445
Problem description: Structural problem
The matrix Hook_1498 is obtained from a 3D mechanical problem discretizing
a steel hook with tetrahedral Finite Elements. The computational grid
consists of regularly shaped elements with three displacement unknowns
associated to each node.
StocF-1465:
# equations: 1465137
# non-zeroes: 21005389
Problem description: Flow in porous medium with a stochastic permeabilies
The matrix StocF_1465 is obtained from a fluid-dynamical problem of flow
in porous medium. The computational grid consists of tetrahedral Finite
Elements discretizing an underground aquifer with stochastic
permeabilties. References: [2,8]
References:
[1] M. Ferronato, G. Gambolati, C. Janna, P. Teatini. "Geomechanical
issues of anthropogenic CO2 sequestration in exploited gas fields", Energy
Conversion and Management, 51, pp. 1918-1928, 2010.
[2] C. Janna, M. Ferronato. "Adaptive pattern research for block FSAI
preconditionig". SIAM Journal on Scientific Computing, to appear.
[3] 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.
[4] 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.
[5] 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.
[6] 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.
[7] C. Janna, A. Comerlati, G. Gambolati. "A comparison of projective and
direct solvers for finite elements in elastostatics". Advances in
Engineering Software, 40, pp. 675-685, 2009.
[8] M. Ferronato, C. Janna, G. Pini. "Shifted FSAI preconditioners for the
efficient parallel solution of non-linear groundwater flow models".
International Journal for Numerical Methods in Engineering, to appear.
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Cube_Coup_* and Long_Coup_* matrices:
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Authors: Carlo Janna and Massimiliano Ferronato
Cube_Coup_*: Symmetric Indefinite Matrix
# equations: 2,164,760
# non-zeroes: 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 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 Cube_Coup_* matrices are symmetric indefinite.
Long_Coup_*: 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 on the 4 matrices 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.
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Janna/CoupCons3D
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Authors: Carlo Janna, Massimiliano Ferronato Giorgio Pini
Matrix type: Unsymmetric
# equations: 416,800
# non-zeroes: 22,322,336
Problem description: Fully coupled poroelastic problem
(structural problem)
The matrix CoupCons3D has been obtained through a Finite Element
transient simulation of a fully coupled consolidation problem on
a three-dimensional domain using Finite Differences for the
discretization in time.
Further information can be found in the following papers:
1) M. Ferronato, G. Pini, and G. Gambolati. The role of
preconditioning in the solution to FE coupled consolidation
equations by Krylov subspace methods. International Journal for
Numerical and Analytical Methods in Geomechanics 33 (2009), pp.
405-423.
2) M. Ferronato, C. Janna, and G. Pini. Parallel solution to
ill-conditioned FE geomechanical problems. International Journal
for Numerical and Analytical Methods in Geomechanics 36 (2012),
pp. 422-437.
3) M. Ferronato, C. Janna and G. Pini. A generalized Block FSAI
preconditioner for unsymmetric indefinite matrices. Journal of
Computational and Applied Mathematics (2012), submitted.
Authors: Carlo Janna, Massimiliano Ferronato, Giorgio Pini
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Janna/ML_Laplace
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Authors: Carlo Janna, Massimiliano Ferronato Giorgio Pini
Matrix type: Unsymmetric
# equations: 377,002
# non-zeroes: 27,689,972
Problem description: Poisson problem
The matrix ML_Laplace has been obtained by discretizing a 2D
Poisson equation with a Meshless Local Petrov-Galerkin method.
Further information can be found in the following papers:
1) G. Pini, A. Mazzia, and F. Sartoretto. Accurate MLPG solution
of 3D potential problems. CMES - Computer Modeling in Engineering
& Sciences 36 (2008), pp. 43-64.
2) M. Ferronato, C. Janna and G. Pini. A generalized Block FSAI
preconditioner for unsymmetric indefinite matrices. Journal of
Computational and Applied Mathematics (2012), submitted.
Authors: Carlo Janna, Massimiliano Ferronato, Giorgio Pini
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Janna/Transport
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Authors: Carlo Janna, Massimiliano Ferronato Giorgio Pini
Matrix type: Unsymmetric
# equations: 1,602,111
# non-zeroes: 23,500,731
Problem description: 3D Finite Element flow and transport
The matrix Transport has been obtained by a FE tetrahedral
discretization of a density driven coupled flow and transport.
Further information can be found in the following papers:
1) A. Mazzia, and M. Putti. High order Godunov mixed methods on
tetrahedral meshes for density driven flow simulations in porous
media. Journal of Computational Physics 208 (2005), pp. 154-174.
2) M. Ferronato, C. Janna and G. Pini. A generalized Block FSAI
preconditioner for unsymmetric indefinite matrices. Journal of
Computational and Applied Mathematics (2012), submitted.
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Janna/ML_Geer
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Authors: Carlo Janna, Massimiliano Ferronato, Giorgio Pini
Matrix type: Unsymmetric
# equations: 1,504,002
# non-zeroes: 110,879,972
Problem description: Poroelastic problem (structural problem)
The matrix ML_Geer has been obtained to find through a Meshless
Petrov-Galerkin discretization the deformed configuration of an
axial-symmetric porous medium subject to a pore-pressure drawdown.
Further information can be found in the following papers:
1) M. Ferronato, A. Mazzia, G. Pini, and G. Gambolati. A meshless
method for axi-symmetric poroelastic simulations: numerical
study. International Journal for Numerical Methods in Engineering
70 (2007), pp. 1346-1365.
2) M. Ferronato, C. Janna and G. Pini. A generalized Block FSAI
preconditioner for unsymmetric indefinite matrices. Journal of
Computational and Applied Mathematics (2012), submitted.
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Bump_2991
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Matrix Name: Bump_2911
Authors: Carlo Janna and Massimiliano Ferronato
Symmetric Positive Definite Matrix
# equations: 2,911,419
# non-zeroes: 130,378,257
Problem description: 3D geomechanical reservoir simulation
The matrix Bump_2911 is obtained from the 3D geomechanical
simulation of a gas-reservoir discretized by linear tetrahedral
Finite Elements. The mechanical properties of the medium vary
with the depth and the geological formation. Zero displacement
are applied on bottom and lateral boundary, while a traction-free
top boundary is assumed.
Further information may be found in the following papers:
1) C. Janna, M. Ferronato, G. Gambolati. "Enhanced Block FSAI
preconditioning using Domain Decomposition techniques". SIAM
Journal on Scientific Computing, 35, pp. S229-S249, 2013.
2) C. Janna, M. Ferronato, G. Gambolati. "The use of supernodes
in factored sparse approximate inverse preconditioning". SIAM
Journal on Scientific Computing, submitted.
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Queen_4147
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Matrix Name: Queen_4147
Authors: Carlo Janna and Massimiliano Ferronato
Symmetric Positive Definite Matrix
# equations: 4,147,110
# non-zeroes: 329,499,288
Problem description: 3D structural problem
The matrix Queen_4147 is obtained from the 3D discretizaion
of a structural problem by isoparametric hexahedral Finite
Elements. The solid material is strongly heterogeneous and
several elements exhibit shape distortion thus producing an
ill-conditioned stiffness matrix.
Further information may be found in the following paper:
1) C. Janna, M. Ferronato, G. Gambolati. "The use of supernodes
in factored sparse approximate inverse preconditioning". SIAM
Journal on Scientific Computing, submitted.
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PFlow_742
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Matrix Name: PFlow_742
Authors: Carlo Janna and Massimiliano Ferronato
Symmetric Positive Definite Matrix
# equations: 742,793
# non-zeroes: 37,138,461
Problem description: 3D pressure-temperature evolution
in porous media
The matrix PFlow_742 is obtained from a 3D simulation of the
pressure-temperature field in a multilayered porous media
discretized by hexahedral Finite Elements. The ill-conditioning
of the matrix is due to the strong contrasts in the material
properties fo different layers.
Further information may be found in the following paper:
1) C. Janna, M. Ferronato, G. Gambolati. "The use of supernodes
in factored sparse approximate inverse preconditioning". SIAM
Journal on Scientific Computing, submitted.