$\varphi$-FD : A well-conditioned finite difference method inspired by $\varphi$-FEM for general geometries on elliptic PDEs

This repository contains the code used in the study "$\varphi$-FD : A well-conditioned finite difference method inspired by $\varphi$-FEM for general geometries on elliptic PDEs" Michel Duprez, Vanessa Lleras, Alexei Lozinski, Vincent Vigon, Killian Vuillemot (preprint).

This repository is for reproducibility purposes only

It is "frozen in time" and not maintained. To use our latest $\varphi$-FEM code please refer to the phiFEM repository.

Usage

Prerequisites

• Git,
• Docker/podman.

The image is based on the legacy FEniCS image: quay.io/fenicsproject/stable:latest and the seaborn python library.

Install the image and launch the container

1. Clone this repository in a dedicated directory:

   mkdir phifd/
   git clone https://github.com/PhiFEM/publication_PhiFD.git phifd

2. Download the images from the docker.io registry, in the main directory:

   export CONTAINER_ENGINE=docker
   cd phifd
   sudo -E bash pull-image.sh

3. Launch the container:

   sudo -E bash run-image.sh

Example of usage

From the main directory phifd, launch the $\varphi$-FD example:

python3 phiFD_2D.py

Issues and support

Please use the issue tracker to report any issues.

Authors (alphabetical)

Michel Duprez, Inria Nancy Grand-Est
Vanessa Lleras, Université de Montpellier
Alexei Lozinski, Université de Franche-Comté
Vincent Vignon, Université de Strasbourg
Killian Vuillemot, Université de Montpellier