phiFEM 0.7.0

phiFEM: convenience tools to use the phiFEM immersed boundary finite element method with dolfinx.

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]).

[^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.

phiFEM Pypi webpage

Dependencies

See phifem-env.yml.

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

Installation

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
  

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
  

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/)