RBniCS is an implementation in FEniCS of several reduced order modelling techniques (and, in particular, certified reduced basis method and Proper Orthogonal Decomposition-Galerkin methods) for coercive problems. It is ideally suited for an introductory course on reduced basis methods and reduced order modelling, thanks to an object-oriented approach and an intuitive and versatile python interface. To this end, it has been employed in several doctoral courses on "Reduced Basis Methods for Computational Mechanics".

RBniCS can also be used as a basis for more advanced projects that would like to assess the capability of reduced order models in their existing FEniCS-based software, thanks to the availability of several reduced order methods (such as reduced basis and proper orthogonal decomposition) and algorithms (such as successive constraint method, empirical interpolation method) in the library.

Several tutorials are provided. This software is also a companion of the introductory reduced basis handbook:

J. S. Hesthaven, G. Rozza, B. Stamm. Certified Reduced Basis Methods for Parametrized Partial Differential Equations. SpringerBriefs in Mathematics. Springer International Publishing, 2015

RBniCS requires

• FEniCS (>= 2017.2.0, python 3), with PETSc, SLEPc, petsc4py and slepc4py for computations during the offline stage;
• numpy and scipy for computations during the online stage.

Additional requirements are automatically handled during the setup.

Simply clone the RBniCS public repository:

git clone https://gitlab.com/RBniCS/RBniCS.git

and install the package by typing

python3 setup.py install

If you want to try RBniCS out but do not have FEniCS already installed, you can pull our docker image from Docker Hub. All required dependencies are already installed. RBniCS tutorials and tests are located at

$FENICS_HOME/RBniCS

Several tutorials are provided the tutorials subfolder.

• Tutorial 01: introduction to the capabilities of RBniCS: reduced basis method for (scalar) elliptic problems [tutorial description, tutorial files, jupyter notebook].
• Tutorial 02: introduction to the capabilities of RBniCS: POD-Galerkin method for (vector) elliptic problems [tutorial description, tutorial files, jupyter notebook].
• Tutorial 03: geometrical parametrization [tutorial description, tutorial files, jupyter notebook].
• Tutorial 04: successive constraint method [tutorial description, tutorial files, jupyter notebook].
• Tutorial 05: empirical interpolation methods for non-affine elliptic problems [tutorial description, tutorial files, jupyter notebook].
• Tutorial 06: reduced basis and POD-Galerkin methods for parabolic problems [tutorial files].
• Tutorial 07: empirical interpolation methods for nonlinear elliptic problems [tutorial files].
• Tutorial 08: empirical interpolation methods for nonlinear parabolic problems [tutorial files].
• Tutorial 09: reduced order methods for advection dominated elliptic problems [tutorial files].
• Tutorial 10: weighted reduced order methods for uncertainty quantification problems [tutorial files].
• Tutorial 11: 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 [tutorial files].
• Tutorial 12: reduced basis and POD-Galerkin methods for Stokes problems [tutorial files].
• Tutorial 13: reduced basis and POD-Galerkin methods for optimal control problems governed by elliptic equations [tutorial files].
• Tutorial 14: reduced basis and POD-Galerkin methods for optimal control problems governed by Stokes equations [tutorial files].
• Tutorial 15: POD-Galerkin methods for optimal control problems governed by quasi geostrophic equations [tutorial files].
• Tutorial 16: one-way coupling between a fluid dynamics problem based on Stokes and an elliptic equation (e.g., temperature, concentration) [tutorial files].
• Tutorial 17: POD-Galerkin and empirical interpolation methods for Navier-Stokes problems [tutorial files].
• Tutorial 18: POD-Galerkin methods for unsteady Stokes problems [tutorial files].
• Tutorial 19: POD-Galerkin methods for unsteady Navier-Stokes problems [tutorial files].

RBniCS is currently developed and mantained at SISSA mathLab by

• Dr. Francesco Ballarin
• Dr. Alberto Sartori
• Prof. Gianluigi Rozza

in the framework of the AROMA-CFD ERC CoG project. Please see the AUTHORS file for a list of contributors.

Contact us by email for further information or questions about RBniCS, or open an issue on our issue tracker. RBniCS is at an early development stage, so contributions improving either the code or the documentation are welcome, both as patches or merge requests.

If you use RBniCS in your work, please use the following citations to reference RBniCS

@book{HesthavenRozzaStamm2015,
  author    = {Hesthaven, Jan S. and Rozza, Gianluigi and Stamm, Benjamin},
  title     = {Certified Reduced Basis Methods for Parametrized Partial Differential Equations},
  publisher = {Springer International Publishing},
  year      = 2015,
  series    = {SpringerBriefs in Mathematics},
  isbn      = {978-3-319-22469-5}
}

and cite the RBniCS website.

A forthcoming publication will also provide more details on RBniCS.

Like all core FEniCS components, RBniCS is freely available under the GNU LGPL, version 3.