(FEniCS)_ii offers some functionality for using FEniCS for PDEs where you combine equation on one domain with equation on a submanifold embedded in that domain. A mesh for the embedded manifold does not need to consist of entities of the mesh of the domain. Crucial for such PDEs is the notion of the trace - hence the name.

Dependencies

• cbc.block
• FEniCS 2019.1.+ (python3)

Optional dependencies

In some of the demos

• HsMG is a package implementing preconditioners for operators in fractional Sobolev spaces. These are needed to construct robust preconditioners for the interface component of the multiscle/multiphysics
• ULFY is used to construct manufactured

Install

Use pip/distutils or similar. E.g. for dev mode run e.g. pip install -e . or pip install . --user, python3 setup.py install --user

Limitations

• Trace(expr) where expr is not a UFL terminal isn't currently supported
• Point constraints
• MPI parallelism

What it can do

Coupled $X$d-$Y$d, $X >=Y >= 1$ and 3d-2d-1d coupled problems where the trace of terminal (see limitations) is used in the coupling. See demos and apps folders for examples. Please note that the demos/apps often include mesh independent preconditioners or nontrivial physics problem formulations which the authors devolop as part of their research. Much like this code they are in various stages of getting/being published. For citing see below.

Citing

If you use FEniCS_ii for your work please cite our paper