TutorialsΒΆ
RBniCS is accompanied by several tutorials, that can be run on a local installation of the library, or interactively in any web browser either on Google Colab or on ARGOS, the Advanced Reduced Groupware Online Simulation platform, without any required installation.
Thermal block problem
Reduced basis method for (scalar) elliptic problems
Elastic block problem
POD-Galerkin method for (vector) elliptic problems
Geometrical parametrization of a hole
Automatic pull back of problems with affine geometric parametrization
Graetz problem
Stability factor estimation by the successive constraint method. Sample problem with non-homogeneous boundary conditions.
View on GitHub
Run on Google Colab- Case 1: with parameter-independent boundary conditions
- Case 2: with parametrized boundary conditions
Run on ARGOSEmpirical Interpolation Methods for non-affine elliptic problems
Reduced basis method for non-affine problems by Empirical Interpolation Method, Discrete Empirical Interpolation Method and Inefficient Online Projection
Unsteady thermal block problem
Reduced basis and POD-Galerkin methods for (scalar) parabolic problems
View on GitHub- Case 1-RB: homogeneous boundary and initial conditions, reduction with reduced basis method
- Case 1-POD: homogeneous boundary and initial conditions, reduction with POD-Galerkin method
- Case 2-RB: homogeneous boundary conditions, non-homogeneous initial conditions, reduction with reduced basis method
- Case 2-POD: homogeneous boundary conditions, non-homogeneous initial conditions, reduction with POD-Galerkin method
- Case 3-RB: non-homogeneous boundary and initial conditions, reduction with reduced basis method
- Case 3-POD: non-homogeneous boundary and initial conditions, reduction with POD-Galerkin method
Run on Google Colab- Case 1-RB: homogeneous boundary and initial conditions, reduction with reduced basis method
- Case 1-POD: homogeneous boundary and initial conditions, reduction with POD-Galerkin method
- Case 2-RB: homogeneous boundary conditions, non-homogeneous initial conditions, reduction with reduced basis method
- Case 2-POD: homogeneous boundary conditions, non-homogeneous initial conditions, reduction with POD-Galerkin method
- Case 3-RB: non-homogeneous boundary and initial conditions, reduction with reduced basis method
- Case 3-POD: non-homogeneous boundary and initial conditions, reduction with POD-Galerkin method
Run on ARGOSNonlinear elliptic problem
Empirical interpolation methods for nonlinear elliptic problems
Nonlinear parabolic problem
Empirical interpolation methods for nonlinear parabolic problems
Coupled problems
One-way coupling between a fluid dynamics problem based on Stokes and an elliptic equation (e.g., temperature, concentration)
View on GitHub Run on Google Colab Run on ARGOSNavier-Stokes problems
Discrete Empirical Interpolation Method for steady Navier-Stokes problems
Unsteady Navier-Stokes problem
POD-Galerkin methods for unsteady Navier-Stokes problems
Coanda Effect
POD-Galerkin methods for bifurcation problems
Stokes problems
Reduced basis and POD-Galerkin methods for Stokes problems
Stokes optimal control problems
Reduced basis and POD-Galerkin methods for optimal control problems governed by Stokes equations
Coupled problems
One-way coupling between a fluid dynamics problem based on Stokes and an elliptic equation (e.g., temperature, concentration)
View on GitHub Run on Google Colab Run on ARGOSNavier-Stokes problems
Discrete Empirical Interpolation Method for steady Navier-Stokes problems
Unsteady Stokes problem
POD-Galerkin methods for unsteady Stokes problems
Unsteady Navier-Stokes problem
POD-Galerkin methods for unsteady Navier-Stokes problems
Elastic block problem
POD-Galerkin method for (vector) elliptic problems
Thermal subfin problem
Steady-state heat transfer problem through a fin
Elastic contact problem
Idealized contact problem in linear elasticity with friction
Beam bridge problem
Geometrical parametrization applied to the physical phenomena of linear deformation of a bridge.
Elliptic optimal control problems
Reduced basis and POD-Galerkin methods for optimal control problems governed by elliptic equations
Stokes optimal control problems
Reduced basis and POD-Galerkin methods for optimal control problems governed by Stokes equations
Optimal control problems governed by the quasi geostrophic equations
POD-Galerkin methods for optimal control problems governed by quasi geostrophic equations
Advection dominated problems
Reduced order models for advection dominated problems
View on GitHub- Case 1-RB
- Case 1-POD
- Case 1-RB with rectification
- Case 1-RB with vanishing viscosity
- Case 2-RB
- Case 2-POD
- Case 3-RB
- Case 3-POD
Run on Google Colab- Case 1-RB
- Case 1-POD
- Case 1-RB with rectification
- Case 1-RB with vanishing viscosity
- Case 2-RB
- Case 2-POD
- Case 3-RB
- Case 3-POD
Run on ARGOSUncertainty quantification problems
Weighted reduced order methods for uncertainty quantification problems
Quasi geostrophic equations
POD-Galerkin methods for quasi geostrophic equations, as an example on how to customize and extend RBniCS beyond the set of problems provided in the core of the library
Optimal control problems governed by the quasi geostrophic equations
POD-Galerkin methods for optimal control problems governed by quasi geostrophic equations