Finite Element Toolkit

This repository is a template and toolkit for undertaking finite element analysis using open source tools. Currently the scope of the reposity covers:

• Defining geometry using cadquery
• Meshing using gmsh
• FEA using dolphinx/fenicsx
• Visualisation using pyvista

By cloning the repository and using the setup defined in the Makefile, you should be able to set up a working finite element analysis simulation environment directly. This is performed using pixi and uv to define the dependencies — as long as these tools are available for your system this workflow should ‘just work’.

Documentation

Alongside the environment setup, a variety of examples and tests are provided to demonstrate functionality and ensure the toolchains are working. Some didactic/formal documentation of the theory is also provided, but you should take this with a grain of salt — I don't know anywhere near as much about the finite element method as the people who have written these tools.

Theory Document

A didactic introduction to the Finite Element Method (FEM) and its implementation in FEniCSx is available in the theory/ folder.

View / Download PDF

Quarto Example

A hands-on walkthrough of a 1-D Poisson problem solved with pure NumPy (no FEM library required) is in the quarto/ folder. The document includes code, maths, and a plot, and is rendered via Quarto.

View Quarto document

Manual installation steps

I use a Mac, this will likely colour some of the steps (e.g. using python3 instead of python).

1. Install pixi:

curl -fsSL https://pixi.sh/install.sh | bash

2. Initialise pixi:

pixi init .

3. Add fenicsx and other dependencies:

pixi install

These dependencies are defined in pixi.toml.

4. There are two ways to execute using pixi. The first is to enter pixi shell and use standard CLI methods within it. The second approach, which is my preference, is to call pixi run as a prefix to the standard commands. To start, install the necessary uv requirements:

pixi run uv pip install -e . --system

Add to these in the pyproject.toml file.

5. If all has gone well, check that everything is installed:

pixi run python3 -c "import dolfinx; print(dolfinx.__version__)"

6. Now you can run an example file:

pixi run mpirun -n 4 python3 minimal_example.py

(minimal_example.py is in the repo already)

The steps above are hard-coded into the Makefile:

make quickstart

You can then delete all of the installed files and start from fresh using

make uninstall