phiFEM: a convenience package for using $\varphi$-FEM with FEniCSx

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

$\varphi$-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 $\varphi$-FEM can be found in the various publications (see e.g. ¹ and ²).

phiFEM Pypi webpage

Dependencies

See phifem-env.yml.

⚠️ Note that all these dependencies (except phifem) are already included in dolfinx Docker container.

Installation

Pixi environment

• Given the pixi.lock file in the source directory, create and run a phifem Pixi environment via:

  pixi shell

Conda environment

• Create a phifem Conda environment from the spec file phifem-env.yml:

  conda create -f phifem-env.yml

• Activate the phifem environment:

  conda activate phifem

Docker container

The phiFEM package can be used 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 phiFEM via pip:

  pip install phifem

Usage

See here.

Run the demos

The demos can be found on the phiFEM Github repository. To run the demos first clone the repository.

Inside the Docker container/Conda environment:

• Install the demos dependencies:

  XXX install polars Pyaml

  with XXX=pip in the Docker container and XXX=conda in the conda environment.

• Navigate the demo directory and run it e.g.:

  cd demo/weak-dirichlet/flower
  python main.py bg

⚠️ The demo files require arguments, for more info run python main.py -h.

Run the tests

Inside the Docker container/Conda environment:

• Install pytest:

  XXX install pytest

  with XXX=pip in the Docker container and XXX=conda in the Conda environment.

• Run the tests:

  cd tests
  pytest

Disclaimer

The author Raphaël Bulle guarantees that his contributions to this project are generative-ai-free.

For more information, see here (in french).

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/.

Logo credit

Frédérique Lecourtier (https://mimesis.inria.fr/members/frederique-lecourtier/)

Footnotes

1. M. DUPREZ and A. LOZINSKI, $\varphi$-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, $\varphi$-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. ↩