multiphenics is a python library that aims at providing tools in FEniCS for an easy prototyping of multiphysics problems on conforming meshes. In particular, it facilitates the definition of subdomain/boundary restricted variables and enables the definition of the problem by means of a block structure.

multiphenics requires FEniCS (>= 2017.2.0, python 3) with PETSc and SLEPc.

Simply clone the multiphenics public repository

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

and install the package by typing

python3 setup.py install

Several tutorials are provided in the tutorials subfolder.

• Tutorial 1: block Poisson test case, to introduce the block notation used in the library.
• Tutorial 2: Navier-Stokes problem using block matrices.
• Tutorial 3: weak imposition of Dirichlet boundary conditions by Lagrange multipliers using block matrices and discarding interior degrees of freedom.
• Tutorial 4: computation of the inf-sup constant for a Stokes problem assembled using block matrices.
• Tutorial 5: computation of the inf-sup constant for the problem presented in tutorial 3.
• Tutorial 6: several examples on optimal control problems, with different state equations (elliptic, Stokes, Navier-Stokes), control (distributed or boundary) and observation (distributed or boundary).
• Additional tutorials on simple multiphysics problems are forthcoming.

multiphenics is currently developed and maintained at SISSA mathLab by Dr. Francesco Ballarin, under the supervision of 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 multiphenics, or open an issue on our issue tracker. multiphenics is at an early development stage, so contributions improving either the code or the documentation are welcome, both as patches or merge requests.

• CBC.Block for the definition of block matrices and vectors in FEniCS.
• multimesh support in FEniCS, which aims at providing support for problems on non conforming meshes. In multiphenics we are rather interested in conforming meshes, with possible restriction of the unknowns to subdomains and/or boundaries.
• MatNest support in FEniCS. In multiphenics we always assemble block matrices into a monolithic matrix, rather then relying on MatNest.
• CutFEM, an unfitted finite element framework for multi-physics problems that relies on the FEniCS project.
• Weak imposition of Dirichlet Dirichlet boundary conditions by Lagrange multipliers is a frequently asked question on FEniCS support forums [1, 2]. Some answers provide possible solutions to the problem (e.g. constraining the useless degrees of freedom by DirichletBC), which however may result in an unnecessarily large system to be solved. multiphenics handles subdomain/boundary restricted variables in an efficient and automatic way.
• Please contact us by email if you have other related resources.

If you use multiphenics in your work, please cite the multiphenics website.

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