Implementing network models in FEniCS

The graphnics library solves network models using the finite element method. This is facilitated via the FenicsGraph class which is an extension of the DiGraph class in networkx.

Demos

• Introduction to Graphnics.
• Pulsatile flow in rat tumour vasculature
• Vasomotion in arterial trees
• Solving coupled 3d-1d network models using fenics_ii

Runtimes

The library fenics_ii has been used for the implementation as it provides rapid and robust assembly of mixed-dimensional problems. The runtimes for the most computationally expensive model is shown here:

• Profiling

Dependencies and installation

The core functionality of graphnics is provided by the following libraries:

• FEniCS version 2019.1.0 or later
• networkx version 2.5 or later

Some of the network flow models require mixed-dimensional assembly, which is provided by the following libraries:

• fenics_ii
• 'cbc.block'

Installation

Provided that these dependencies are installed, graphnics can be pip-installed via

git clone https://github.com/IngeborgGjerde/graphnics/ && cd graphnics
python3 -m pip install .

Should you have trouble installing these dependencies, we recommend you use the below docker image.

Docker image

The full environment for graphnics, along with demos, is provided as a docker container. The container can be built and run locally by executing

git clone https://github.com/IngeborgGjerde/graphnics/
cd graphnics/docker 
docker build --no-cache -t graphnics . # build docker image
cd ..

# make container
docker run --name graphnics-container -v "$(pwd):/home/fenics/shared" -d -p 127.0.0.1:8888:8888 graphnics 'jupyter-notebook --ip=0.0.0.0'

The directory you run the above command from will then be shared with the docker container.

In order to run the jupyter notebook demos, execute

docker logs graphnics-container

in the terminal. This will print a link to the jupyter notebook. Copy the link and paste it into your browser.

To run scripts natively in the container, you can enter the container by running

docker exec -it graphnics-container /bin/bash

and access the shared directory by running

cd shared

Citation

You can cite the repo using arxiv preprint

@article{graphnics2022gjerde,
       author = {{Gjerde}, Ingeborg G.},
        title = "{Graphnics: Combining FEniCS and NetworkX to simulate flow in complex networks}",
      journal = {arXiv e-prints},
         year = 2022,
        month = dec,
archivePrefix = {arXiv},
       eprint = {2212.02916}}