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.

01

Thermal block problem

Reduced basis method for (scalar) elliptic problems

02

Elastic block problem

POD-Galerkin method for (vector) elliptic problems

03

Geometrical parametrization of a hole

Automatic pull back of problems with affine geometric parametrization

04

Graetz problem

Stability factor estimation by the successive constraint method. Sample problem with non-homogeneous boundary conditions.

05

Empirical 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

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Run on Google Colab
  • EIM
  • DEIM
  • Inefficient
Run on ARGOS
06

Unsteady thermal block problem

Reduced basis and POD-Galerkin methods for (scalar) parabolic problems

07

Nonlinear elliptic problem

Empirical interpolation methods for nonlinear elliptic problems

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Run on Google Colab
Run on ARGOS
08

Nonlinear parabolic problem

Empirical interpolation methods for nonlinear parabolic problems

16

Coupled problems

One-way coupling between a fluid dynamics problem based on Stokes and an elliptic equation (e.g., temperature, concentration)

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Run on Google Colab
Run on ARGOS
17

Navier-Stokes problems

Discrete Empirical Interpolation Method for steady Navier-Stokes problems

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Run on Google Colab
Run on ARGOS
19

Unsteady Navier-Stokes problem

POD-Galerkin methods for unsteady Navier-Stokes problems

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Run on Google Colab
Run on ARGOS
12

Stokes problems

Reduced basis and POD-Galerkin methods for Stokes problems

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Run on Google Colab
Run on ARGOS
14

Stokes optimal control problems

Reduced basis and POD-Galerkin methods for optimal control problems governed by Stokes equations

16

Coupled problems

One-way coupling between a fluid dynamics problem based on Stokes and an elliptic equation (e.g., temperature, concentration)

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Run on Google Colab
Run on ARGOS
17

Navier-Stokes problems

Discrete Empirical Interpolation Method for steady Navier-Stokes problems

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Run on Google Colab
Run on ARGOS
18

Unsteady Stokes problem

POD-Galerkin methods for unsteady Stokes problems

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Run on Google Colab
Run on ARGOS
19

Unsteady Navier-Stokes problem

POD-Galerkin methods for unsteady Navier-Stokes problems

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Run on Google Colab
Run on ARGOS
13

Elliptic optimal control problems

Reduced basis and POD-Galerkin methods for optimal control problems governed by elliptic equations

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14

Stokes optimal control problems

Reduced basis and POD-Galerkin methods for optimal control problems governed by Stokes equations

15

Optimal control problems governed by the quasi geostrophic equations

POD-Galerkin methods for optimal control problems governed by quasi geostrophic equations

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Run on Google Colab
Run on ARGOS
09

Advection dominated problems

Reduced order models for advection dominated problems

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  • 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
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Run on ARGOS
10

Uncertainty quantification problems

Weighted reduced order methods for uncertainty quantification problems

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11

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

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15

Optimal control problems governed by the quasi geostrophic equations

POD-Galerkin methods for optimal control problems governed by quasi geostrophic equations

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Run on Google Colab
Run on ARGOS