A collection of Sparse Matrices for the development and performance evaluation of sparse matrix algorithms.
| Id | Name | Rows | Nonzeros | Application | Type | Description | Download File |
|---|---|---|---|---|---|---|---|
| 1 | BUMP_2911 | 2,911,419 | 130,378,257 | 3D geomechanical reservoir simulation | SPD | 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 | Download |
| 2 | EMILIA_923 | 923,136 | 41,005,206 | Geomechanical problem | SPD | 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. | Download |
| 3 | FAULT_639 | 638,802 | 28,614,564 | 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. | Download | |
| 4 | FLAN_1565 | 1,564,794 | 117,406,044 | 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. | Download | |
| 5 | GEO_1438 | 1,437,960 | 63,156,690 | Geomechanical problem | SPD | 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. | Download |
| 6 | HEEL_1138 | 1,138,443 | 51,677,937 | 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. 1526, 2017. | Download | |
| 7 | HOOK_1498 | 1,498,023 | 60,917,445 | 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. 1526, 2017. | Download | |
| 8 | PLOW_742 | 742,793 | 37,138,461 | 3D pressure-temperature evolution in porous media | SPD | 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. A190A219, (2019). | Download |
| 9 | QUEEN_4147 | 4,147,110 | 329,499,288 | 3D structural problem | SPD | 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. | Download |
| 10 | SERENA | 1,391,349 | 64,531,701 | structural problem | SPD | 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. | Download |
| 11 | STOCF_1465 | 1,465,137 | 21,005,389 | 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. | Download | |
| 12 | GUENDA11M | 11,452,398 | 512,484,300 | Geomechanics | SPD | 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. | Download |
| 13 | AGG14M | 14,106,408 | 633,142,730 | Mesoscale simulation | SPD | 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,\nu1) = (25,000MPa,0.30), while the polystyrene inclusions are characterized by (E2,\nu2) = (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. | Download |
| 14 | M20 | 20,056,050 | 1,634,926,088 | Mechanical problem | SPD | 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,\nu) = (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. 281292. [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. | Download |
| 15 | TRIPOD24M | 24,186,993 | 1,111,751,217 | Mechanical problem | SPD | The mesh derives from the 3D mechanical equilibrium of a tripod with clamped bases. Material is linear elastic with (E,\nu) = (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. | Download |
| 16 | RTANIS44M | 44,798,517 | 747,633,815 | Porous flow | SPD | 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(\theta) -sin(\theta) 0 ; sin(\theta) cos(\theta) 0; 0 0 1] and: K = diag(Kx,Ky,Kz) with the rotation angle \theta = 30deg and the permeability coefficients given by Kx = 10.0, Ky = 1.0e-3, Kz = 1.0e-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. | Download |
| 17 | GEO61M | 61,813,395 | 4,966,380,225 | Geomechanics | SPD | 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. | Download |
| 18 | UTEMP20M | 20,113,744 | 242,765,052 | 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. | Download | |
| 19 | PFLOW73M | 73,623,733 | 73,623,733 | 3D pressure evolution in porous media | SPD | 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 Darcys 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. | Download |
| 20 | C4ZZ134M | 134,395,551 | 10,806,265,323 | Biomedicine | SPD | 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,\nu) = (0.06M Pa,0.4) and (E,\nu) = (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. | Download |