- BUMP_2911:
Bump_2911.coo.gz (1.217 GB)
# 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.
[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, 37, pp. C72-C94, 2015.
- CUBE_NNK:
Cube1k.coo.gz (0.001 GB)
Cube14k.coo.gz (0.006 GB)
Cube105k.coo.gz (0.035 GB)
Cube739k.coo.gz (0.326 GB)
Cube5317k.coo.gz (1.999 GB)
# equations: 1,773 to 5,317,443
# non-zeroes: 63,927 to 222,615,369
Problem description: 3D homogeneus elasticity problem
The matrices Cube_nnk have been obtained through the FE
dicretization of the elasticity problem of a cube with linear
tetrahedrons. The material property is constant on the
domain and the Poisson ratio is assumed equal to 0.3.
The sequence of matrices is generated by subsequent refinement of
the original grid (that is each tet is divided in 8) with the number
and location of boundary conditions fixed. Only 60 unknowns are
prescribed meaning that the body is only "loosely" constrained from
an algebraic viewpoint.
- EMILIA_923:
Emilia_923.coo.gz (0.272 GB)
# 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.
[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, 33 (6), pp. 3357-3380, 2011.
- FAULT_639:
Fault_639.coo.gz (0.333 GB)
# 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 [1,2,3,4]
[1] 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.
[2] 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.
[3] 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.
[4] 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.
- FLAN_1565:
Flan_1565.coo.gz (0.651 GB)
# 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.
[1] 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.
[2] 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.
- GEO_1438:
Geo_1438.coo.gz (0.705 GB)
# 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.
[1] 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.
- HEEL_1138:
Heel_1138.coo.gz (0.510 GB)
# equations: 1138443
# non-zeroes: 51677937
Problem description: Structural problem
The matrix Heel_1138 is obtained from a 3D mechanical problem discretizing
a heel with tetrahedral Finite Elements. The computational grid
consists of regularly shaped elements with three displacement unknowns
associated to each node.
[1] R. Baggio, A. Franceschini, N. Spiezia, C. Janna. "Rigid body modes deflation of the
Preconditioned Conjugate Gradient in the solution of discretized structural problems".
Computers & Structures, 185, pp. 15–26, 2017.
- HOOK_1498:
Hook_1498.coo.gz (0.516 GB)
# 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.
[1] R. Baggio, A. Franceschini, N. Spiezia, C. Janna. "Rigid body modes deflation of the
Preconditioned Conjugate Gradient in the solution of discretized structural problems".
Computers & Structures, 185, pp. 15–26, 2017.
- PFLOW_742:
PFlow_742.coo.gz (0.466 GB)
# 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.
[1] C. Janna, M. Ferronato, G. Gambolati. "The use of supernodes
in factored sparse approximate inverse preconditioning". SIAM
Journal on Scientific Computing, 37, pp. C72-C94, 2015.
[2] V. A. Paludetto Magri, A. Franceschini, C. Janna. "A Novel Algebraic Multigrid
Approach Based on Adaptive Smoothing and Prolongation for Ill-Conditioned Systems".
SIAM Journal on Scientific Computing, 41(1), pp. A190–A219, (2019).
- QUEEN_4147:
Queen_4147.coo.gz (3.131 GB)
# 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.
[1] C. Janna, M. Ferronato, G. Gambolati. "The use of supernodes
in factored sparse approximate inverse preconditioning". SIAM
Journal on Scientific Computing, 37, pp. C72-C94, 2015.
- SERENA:
Serena.coo.gz (0.614 GB)
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.
[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.
- STOCF_1465:
StocF_1465.coo.gz (0.216 GB)
# equations: 1,465,137
# non-zeroes: 21,005,389
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.
[1] C. Janna, M. Ferronato. "Adaptive pattern research for block FSAI
preconditionig". SIAM Journal on Scientific Computing, 33 (6), pp. 3357-3380, 2011.
[2] 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, 89, pp. 1707-1719, 2012.
- GUENDA11M:
guenda11m.tar.bz2 (4.693 GB)
# equations: 11,452,398
# non-zeroes: 512,484,300
Problem description: Geomechanics
The matrix guenda11m derives from a domain that spans an area of
40 × 40 km2 and extends down to 5 km depth. To reproduce with high fidelity the
real geometry of the gas reservoir, a severely distorted mesh with 22,665,896 linear
tetrahedra and 3,817,466 vertices is used. While fixed boundaries are prescribed on
the bottom and lateral sides, the surface is traction-free.
[1] A. Franceschini, V. A. Paludetto Magri, G. Mazzucco, N. Spiezia, and C. Janna.
"A robust adaptive algebraic multigrid linear solver for structural mechanics".
Computer Methods in Applied Mechanics and Engineering, 352, pp. 389-416, 2019.
[2] G. Isotton, M. Frigo, N. Spiezia, C. Janna. "Chronos: A general purpose
classical amg solver for high performance computing".
arXiv:2102.07417 [math.NA], 2021.
[3] G. Isotton, M. Bernaschi, C. Janna. "A GPU-accelerated adaptive FSAI preconditioner
for massively parallel simulations", arXiv:2010.14175 [math.NA], 2021.
- AGG14M:
agg14m.tar.bz2 (5.364 GB)
# equations: 14,106,408
# non-zeroes: 633,142,730
Problem description: Mesoscale simulation
The mesh derives from a 3D mesoscale simulation of an heterogeneous cube of
lightened concrete. The domain has dimensions 50 × 50 × 50 mm3 and contains 2,644
spherical inclusions of polystyrene. The cement matrix is characterized by
(E1,ν1) = (25,000MPa,0.30), while the polystyrene inclusions are characterized by
(E2,ν2) = (5MPa,0.30). Hence, the contrast between the Young modules of these two
linear elastic materials is extremely high. The discretization is done via
tetrahedral finite elements.
[1] G. Mazzucco, B. Pomaro, V. Salomoni, C. Majorana. "Numerical modelling of
ellipsoidal inclusions". Construction and Building Materials, 167, pp. 317-324,
2018.
[2] G. Mazzucco, B. Pomaro, G. Xotta, C. E. Maiorana, V. A. Salomoni. "Tomography
reconstruction of concrete materials for mesoscale modelling". Engineering
Computations, 2020.
[3] A. Franceschini, V. A. Paludetto Magri, G. Mazzucco, N. Spiezia, and C. Janna.
"A robust adaptive algebraic multigrid linear solver for structural mechanics".
Computer Methods in Applied Mechanics and Engineering, 352, pp. 389-416, 2019.
[4] G. Isotton, M. Frigo, N. Spiezia, C. Janna. "Chronos: A general purpose
classical amg solver for high performance computing".
arXiv:2102.07417 [math.NA], 2021.
[5] G. Isotton, M. Bernaschi, C. Janna. "A GPU-accelerated adaptive FSAI preconditioner
for massively parallel simulations", arXiv:2010.14175 [math.NA], 2021.
- M20:
M20.tar.bz2 (12.619 GB)
# equations: 20,056,050
# non-zeroes: 1,634,926,088
Problem description: Mechanical problem
The mesh derives from the 3D mechanical equilibrium of a symmetric machine
cutter that is loosely constrained. The unstructured mesh is composed
by 4,577,974 second order tetrahedra and 6,713,144 vertices resulting in 20,056,050
DOFs. Material is linear elastic with (E,ν) = (108 MPa,0.33). This problem was
initially presented by [1] and later used in the works [2,3,4].
[1] S. Koric, Q. Lu, E. Guleryuz. "Evaluation of massively parallel linear sparse
solvers on unstructured finite element meshes". Computers & Structures, 141 (2014),
pp. 19 – 25.
[2] S. Koric, A. Gupta. "Sparse matrix factorization in the implicit finite
element method on petascale architecture". Computer Methods in Applied Mechanics
and Engineering, 302 (2016), pp. 281–292.
[3] A. Franceschini, V. A. Paludetto Magri, G. Mazzucco, N. Spiezia, and C. Janna.
"A robust adaptive algebraic multigrid linear solver for structural mechanics".
Computer Methods in Applied Mechanics and Engineering, 352, pp. 389-416, 2019.
[4] G. Isotton, M. Frigo, N. Spiezia, C. Janna. "Chronos: A general purpose
classical amg solver for high performance computing".
arXiv:2102.07417 [math.NA], 2021.
- TRIPOD24M:
tripod24m.tar.bz2 (9.373 GB)
# equations: 24,186,993
# non-zeroes: 1,111,751,217
Problem description: Mechanical problem
The mesh derives from the 3D mechanical equilibrium of a tripod with clamped
bases. Material is linear elastic with (E,ν) = (106MPa,0.45).
The mesh is formed by linear tetrahedra and discretization is given by the finite
element method.
[1] A. Franceschini, V. A. Paludetto Magri, G. Mazzucco, N. Spiezia, and C. Janna.
"A robust adaptive algebraic multigrid linear solver for structural mechanics".
Computer Methods in Applied Mechanics and Engineering, 352, pp. 389-416, 2019.
[2] G. Isotton, M. Frigo, N. Spiezia, C. Janna. "Chronos: A general purpose
classical amg solver for high performance computing".
arXiv:2102.07417 [math.NA], 2021.
- RTANIS44M:
rtanis44m.coo.bz2 (X.373 GB)
# equations: 44,798,517
# non-zeroes: 747,633,815
Problem description: Porous flow
The mesh derives from a 3D diffusion problem in a porous media. The diffusion
problem is governed by an anisotropic permeability tensor of the form K = Q'*K*Q,
where Q is a rotation matrix and K is a diagonal matrix defined, in MATLAB
notation, as:
Q = [cos(θ) -sin(θ) 0 ; sin(θ) cos(θ) 0; 0 0 1]
and:
K = diag(Kx,Ky,Kz)
with the rotation angle θ = 30◦ and the permeability coefficients given by
Kx = 10.0, Ky = 1.0−3, Kz = 1.0−6.
[1] G. Isotton, M. Frigo, N. Spiezia, C. Janna. "Chronos: A general purpose
classical amg solver for high performance computing".
arXiv:2102.07417 [math.NA], 2021.
- GEO61M:
geo61m.tar.bz2 (41.737 GB)
# equations: 61,813,395
# non-zeroes: 4,966,380,225
Problem description: Geomechanics
The matrix geo61m represents a geological formation with 479 layers. The geometry
of the modeled domain is characterized by an area of 55 × 40 km2 with the reservoir
in an almost barycentric position and the base at a depth of 6.5km. The grid is
based on a mesh of 20,354,736 brick elements. Some elements are highly distorted
to reproduce the geological layers accurately.
[1] A. Franceschini, V. A. Paludetto Magri, G. Mazzucco, N. Spiezia, and C. Janna.
"A robust adaptive algebraic multigrid linear solver for structural mechanics".
Computer Methods in Applied Mechanics and Engineering, 352, pp. 389-416, 2019.
[2] G. Isotton, M. Frigo, N. Spiezia, C. Janna. "Chronos: A general purpose
classical amg solver for high performance computing".
arXiv:2102.07417 [math.NA], 2021.
[3] G. Isotton, M. Bernaschi, C. Janna. "A GPU-accelerated adaptive FSAI preconditioner
for massively parallel simulations", arXiv:2010.14175 [math.NA], 2021.
- UTEMP20M:
Utemp20m.coo.bz2 (2.102 GB)
# equations: 20,113,744
# non-zeroes: 242,765,052
Problem description: Temperature diffusion in heterogeneous medium
The mesh derives from the simulation of temperature diffusion in a highly
heterogeneous geological formation. The domain size has a regional scale with an
areal extension of several thousands of km2. Most of the elements presents a bad
aspect ratio due to the need of accurately represent the geological sequences.
- PFLOW73M:
Pflow73m.coo.bz2 (21.161 GB)
# equations: 73,623,733
# non-zeroes: 2,201,828,891
Problem description: 3D pressure evolution in porous media
The mesh derives from a basin model, with the discretization of a 178.8×262.0 km2
geological area - at the end of basin evolution - with a mesh of 20-node hexahedral
elements. The Pflow73m matrix derives from the discretization of the mass
conservation and Darcy’s law. Due to strong permeability contrasts between neighboring
elements and geometrical distortion of the computational grid, the matrix is severely
ill-conditioned and challenging to solve.
[1] A. Franceschini, V. A. Paludetto Magri, G. Mazzucco, N. Spiezia, and C. Janna.
"A robust adaptive algebraic multigrid linear solver for structural mechanics".
Computer Methods in Applied Mechanics and Engineering, 352, pp. 389-416, 2019.
[2] G. Isotton, M. Frigo, N. Spiezia, C. Janna. "Chronos: A general purpose
classical amg solver for high performance computing".
arXiv:2102.07417 [math.NA], 2021.
[3] G. Isotton, M. Bernaschi, C. Janna. "A GPU-accelerated adaptive FSAI preconditioner
for massively parallel simulations", arXiv:2010.14175 [math.NA], 2021.
- C4ZZ134M:
c4zz134m.tar.bz2 (78.471 GB)
# equations: 134,395,551
# non-zeroes: 10,806,265,323
Problem description: Biomedicine
The mesh derives from the discrtization of the complex conformation of the urethral
duct, with particular regard to the bulbar region. The duct locally consists of an
inner thin layer of dense connective tissue and an outer thick stratum of more
compliant spongy tissue. Both the materials are linear elastic, characterized by
(E,ν) = (0.06M Pa,0.4) and (E,ν) = (0.0066M Pa,0.4), respectively.
[1] A.N. Natali, E.L. Carniel, C.G. Fontanella, A.Frigo, S.Todros, A.Rubini,
G.M. De Benedictis, M.A. Cerruto, W. Artibani. "Mechanics of the urethral duct:
tissue constitutive formulation and structural modeling for the investigation of
lumen occlusion". Biomechanics and modeling in mechanobiology, 16(2), pp. 439-447,
2017.
[2] A.N. Natali, E.L. Carniel, C.G. Fontanella, S.Todros, G.M. De Benedictis, M.A. Cerruto,
W. Artibani. "Urethral lumen occlusion by artificial sphincteric devices: a
computational biomechanics approach". Biomechanics and modeling in mechanobiology,
16(4), pp. 1439-1446, 2017.
[3] G. Isotton, M. Frigo, N. Spiezia, C. Janna. "Chronos: A general purpose
classical amg solver for high performance computing".
arXiv:2102.07417 [math.NA], 2021.
[4] G. Isotton, M. Bernaschi, C. Janna. "A GPU-accelerated adaptive FSAI preconditioner
for massively parallel simulations", arXiv:2010.14175 [math.NA], 2021.
