phiFEM: a convenience package for using φ-FEM with FEniCSx

This package provides convenience tools that help with the implementation of φ-FEM schemes in the FEniCSx computation platform.

φ-FEM (or phiFEM) is an immersed boundary finite element method leveraging levelset functions to avoid the use of any non-standard finite element spaces or non-standard quadrature rules near the boundary of the domain. More information about φ-FEM can be found in the various publications (see e.g. 1 and 2).

Prerequisites

Usage

We recommend to use phiFEM inside the dolfinx container (e.g. ghcr.io/fenics/dolfinx/dolfinx:stable).

  • Launch the dolfinx container in interactive mode using, e.g. Docker (see the docker documentation for the meaning of the different arguments):

    docker run -ti -v $(pwd):/home/dolfinx/shared -w /home/dolfinx/shared dolfinx/dolfinx:stable

  • Inside the container install the phiFEM package with pip:

    pip install phifem

Run the demos

The demos can be found on the phiFEM Github repository. To run the demos you’ll need to clone the repository and build and launch the container:

  1. Clone the phiFEM repository:
git clone https://github.com/PhiFEM/phiFEM.git
  1. Build the container (you might need sudo privileges):
cd phifem/docker
bash build_image.sh
  1. Run the container (you might need sudo privileges):
cd ../
bash run_image.sh
  1. Inside the containern navigate the demo directory and e.g. run the interface elasticity demo:
cd demo/interface-elasticity
python main param1

Run the tests

To run the tests, follow the steps 1 to 3 to run the demos and inside the container:

cd tests
pytest

License

phiFEM is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with phiFEM. If not, see http://www.gnu.org/licenses/.

Authors (alphabetical)

Raphaël Bulle (https://rbulle.github.io)
Michel Duprez (https://michelduprez.fr/)
Killian Vuillemot

Footnotes

  1. M. DUPREZ and A. LOZINSKI, \(\phi\)-FEM: A finite element method on domains defined by level-sets, SIAM J. Numer. Anal., 58 (2020), pp. 1008-1028, https://epubs.siam.org/doi/10.1137/19m1248947↩︎

  2. S. COTIN, M. DUPREZ, V. LLERAS, A. LOZINSKI, and K. VUILLEMOT, \(\phi\)-FEM: An efficient simulation tool using simple meshes for problems in structure mechanics and heat transfer, Partition of Unity Methods, (2023), pp. 191-216, https://www.semanticscholar.org/paper/%CF%86-FEM%3A-an-efficient-simulation-tool-using-simple-in-Cotin-Duprez/82f2015ac98f66af115ae57f020b0b1a45c46ad0,↩︎