Snakemake workflow for solving system of Poisson-Nernst-Planck equations on 2d domains with one rough boundary.

This workflow uses

• F. Mölder et al., “Sustainable data analysis with Snakemake,” Apr. 19, 2021, F1000Research: 10:33. doi: 10.12688/f1000research.29032.2.

to stitch together

• I. A. Baratta et al., “DOLFINx: the next generation FEniCS problem solving environment.” 2023. doi: 10.5281/zenodo.10447666.
• J. S. Dokken, “ADIOS4DOLFINx: A framework for checkpointing in FEniCS,” Journal of Open Source Software, vol. 9, no. 96, p. 6451, Apr. 2024, doi: 10.21105/joss.06451.
• C. Geuzaine and J.-F. Remacle, “Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities,” International Journal for Numerical Methods in Engineering, vol. 79, no. 11, pp. 1309–1331, 2009, doi: 10.1002/nme.2579.
• P. Grigorev et al., “matscipy: materials science at the atomic scale with Python,” Journal of Open Source Software, vol. 9, no. 93, p. 5668, Jan. 2024, doi: 10.21105/joss.05668.
• M. C. Röttger et al., “Contact.engineering—Create, analyze and publish digital surface twins from topography measurements across many scales,” Surf. Topogr.: Metrol. Prop., vol. 10, no. 3, p. 035032, Sep. 2022, doi: 10.1088/2051-672X/ac860a.

for modeling and analyzing the electrochemical double layer on rough line profiles.

Raw profiles are found within in/profiles.

Profile-specific configuration and assignment of unique labels happens within workflow/config.yml.

Content of output directory:

all.csv  # homogenized global properties of all systems
figures  # publication-quality figures of global properties
geometries  # 2d geometries generated from line scan profiles
global_properties_plots  # plots of global properties
meshes  # meshes generated from geometries
potential_0.005  # sweep across potential values
potential_0.01
...
potential_0.18
potential_0.2
profiles  # homogenized line scan profiles

Within each potential_* subfolder, the following folders contain polished figures:

• plot_solution_1d: illustration of 1d double layer

• plot_solution_2d_global: color maps of potential and concentrations on whole domain

• plot_solution_2d_local: color maps of potential and concentrations on small subdomain

• surface_excess_global_plots: surface excess on whole domain

• surface_excess_local_plots: surface excess on small subdomain

• comparative_plots: plots comparing global scalar profile-specific properties

Other folders contain intermediate or final results.

• checkpoint: immediate, dimensionless solution of PNP system
• comparative_properties: global scalar profile-specific properties with respect to reference profile
• derived_properties: global scalar profile-specific properties derived from FEM solution
• geometries: domain geometries generated from profiles
• interpolation: dimensionless solution of PNP system interpolated down to 1st order Lagrange elements for visualization
• profile_properties: global scalar profile-specific properties derived from profiles alone
• surface_charge: results from surface charge compuaton
• surface_integrals: results from integration of variables in z direction
• volume_integrals: results from integration over whole domain

To build a container image based on the fenicsx tutorials container that includes additional packages necessary to run this workflow, run

docker build -t imteksim/dolfinx-tutorial-extended -f container/dolfinx-tutorial-extended/Dockerfile .

from within the repository root.

The container runs in the same manner as the tutorial container itself,

docker run -v $(pwd):/tmp/data --init -ti -p 8888:8888 imteksim/dolfinx-tutorial-extended

To install development versions of git repositories within container, mark dirctory as safe, i.e. with

git config --global --add safe.directory /tmp/data/matscipy

before running

pip install .

For an editable install of matscipy, use

pip install meson-python
pip install --no-build-isolation -e .

Use

snakemake --cores all --verbose

to run all analysis.

Create directed acyclic graphs of the workflow with

snakemake --dag | dot -Tsvg > dag_all.svg
snakemake --rulegraph | dot -Tsvg > rulegraph.svg
snakemake --filegraph | dot -Tsvg > filegraph.svg

To be able to interactively edit a notebook with a command like

snakemake --cores 1 --edit-notebook out/figures/surplus_surface_excess_potential_bias.svg --notebook-listen 0.0.0.0:8889

launch the conainer embedding snakemake with additional ports open first, e.g.

docker run -v $(pwd):/tmp/data --init -ti -p 8888:8888 -p 8889:8889 imteksim/dolfinx-tutorial-extended

Generate a jupyter configuration with

# jupyter notebook --generate-config
Writing default config to: /root/.jupyter/jupyter_notebook_config.py

and append the lines

echo "c.ServerApp.allow_root = True" >> /root/.jupyter/jupyter_notebook_config.py
# echo "c.NotebookApp.ip = '0.0.0.0'" >> /root/.jupyter/jupyter_notebook_config.py

to the config file.

Launch a display server before running snakemake, e.g. with

export DISPLAY=:99.0
export PYVISTA_OFF_SCREEN=true
Xvfb :99 -screen 0 1024x768x24 > /dev/null 2>&1 &

Use matplotlibrc in repository with

export MATPLOTLIBRC="$(pwd)/matplotlibrc"

before running plotting scripts.

Install Arial with

apt update
apt install ttf-mscorefonts-installer