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redbKIT
a MATLAB library for reduced-order modeling of PDEs

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)