phiFEM 0.4.2

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

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

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. More information about φ-FEM can be found in the various publications (see e.g. [^1] and [^2]).

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

[^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,

Prerequisites

General

• dolfinx

To run some of the demos

• PyYAML

To run the tests

• pytest

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

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