Problems Gallery
The Problems
folder contains a gallery of tests, examples and applications which are listed below (if a problem is marked as included in the testsuite, it means that it is tested by the test_all.m
function).
FEM-ADR: Advection-diffusion-reaction equations
FEM_TestMetis
test Metis installation for mesh partitioning (included in the testsuite)
FEM_Test_2DLaplacian
test convergence of 2D finite element approximation of the Laplacian in a square domain (included in the testsuite)
FEM_Test_3DLaplacian
test convergence of 3D finite element approximation of the Laplacian in a cube (included in the testsuite)
FEM_Test_ADRt_2D
example of 2D finite element approximation of a time-dependent advection-diffusion-reaction problem (included in the testsuite)
FEM_Test_ADRt_3D
example of 3D finite element approximation of a time-dependent advection-diffusion-reaction problem (included in the testsuite)
FEM-CFD: Fluid dynamics
FEM_CFD_Steady_Test2D
solution of the steady 2D Navier-Stokes equations in a backward-facing step channel
FEM_CFD_Steady_Test3D
solution of the steady 3D Navier-Stokes equations around a bluff body (a description of the geometry is given here)
FEM_CFD_Dfg2D
2D unsteady Navier-Stokes equations: flow around a cylinder benchmark. For a detailed description of this problem see the FeatFlow website. (included in the testsuite)
FEM_CFD_Dfg3D
3D unsteady Navier-Stokes equations: flow around a cylinder benchmark. For a detailed description of this problem see the FeatFlow website. (included in the testsuite)
FEM-CSM: Solid mechanics
FEM_CSM_Test2D
finite element approximation of the 2D steady linear elasticity equations (included in the testsuite)
FEM_CSM_Test3D
finite element approximation of the 3D hyper-elastic equations with Saint Venant-Kirchhoff constitutive law (included in the testsuite)
FEM_CSMt_Test2D
finite element approximation of the 2D nonlinear elastodynamics equations with different constitutive laws (included in the testsuite)
FEM_CSM_ShearCube
finite element approximation of a shear test on a cube with Saint Venant-Kirchhoff material model
FEM_MeshMotion_test2D
mesh deformation of a 2D domain (square with a hole) using the harmonic- and solid-extension mesh motion techniques.
FEM_CSM_Spinning
this problem simulates the fast spinning of an aluminium top in a gravitational field. For a detailed description of the model see (Farhat et al, 2014)
FEM-FSI: Fluid-Structure Interaction
FEM_FSI_Turek2D
numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow. For a detailed description of this problem see the FeatFlow website.
FEM_FSI_ElasticBeam2D
2D flow past an elastic beam attached to a fixed, rigid block. Details can be found here and here.
FEM_FSI_ElasticBeam3D
3D version of the 2D flow past an elastic beam attached to a fixed, rigid block.
FEM_CerebralAneurysm_C0094
fluid-structure interaction simulaiton of the blood flow in a cerebral aneurysm
Reduced Basis Methods
RB_Mixer
RB approximation of the steady heat conduction-convection problem described in Sects. 3.8, 6.6 and 7.2 of [QMN16]
RB_AffineDevice
RB approximation of the steady heat-transfer problem described in Sects. 8.3 and 9.1 of [QMN16] (included in the testsuite)
RB_Beam
RB approximation of the linear elasticity problem described in Sect. 9.2 of [QMN16]
RB_Cookies
RB approximation of the steady diffusion problem described in Sect. 7.5 of [QMN16]
RB_EIM_Gaussian
RB approximation of the nonaffine steady heat-transfer problem described in Sects. 8.4 and 10.5 of [QMN16] (included in the testsuite)
Test_EIM_DEIM
Test and compare EIM and DEIM on the function defined in equation (3.36) of this paper (included in the testsuite)
RB_AcousticHorn_Affine
RB approximation of the (affine) Helmholtz equations modeling the propagation of a pressure wave into an acoustic horn. For a detailed description see [NMA15]
RB_CSM_ShearCube
POD-DEIM approximation of the FEM_CSM_ShearCube
example (finite element approximation of a shear test on a cube with Saint Venant-Kirchhoff material model)
RB_CSM_Turek2D
POD-DEIM approximation of the (time-dependent) structural problem in the FEM_FSI_Turek2D suite
RB - MDEIM
RB_AcousticHorn_NonAffine
RB-MDEIM approximation of the (nonaffine) Helmholtz equations modeling the propagation of a pressure wave into an acoustic horn. The geometry of the horn is parametrized with a Radial Basis Functions mapping. System approximation is performed via the Matrix Discrete Empirical Interpolation method, as detailed in [NMA15]
RB_MeshMotion_Scattering
RB-MDEIM approximation of a 2D scattering problem on a deformable object. For a detailed description of the problem see (Manzoni, Negri, 2016)