All data and source code associated with this research are dedicated to the public domain and are completely free and open-source. Source files for the simulations can be found within Project Elara’s elara-labs repository:

• FreeFEM finite-element simulation files used for the final report can be found within freefem/release/report-1

• findiff finite-difference simulation files used for the final report can be found in notebooks/archived/helmholz-fdm-updated-8-31-2024.ipynb

To be able to run the simulations locally, first clone the repository:

git clone https://codeberg.org/elaraproject/elara-labs
cd elara-labs

Then, install FreeFEM according to their official installation instructions, and ensure you have a fairly recent Python installation (Python 3.10+). Then, simply run:

pip install notebook matplotlib numpy findiff scipy scikit-learn

For running the finite-element simulations, from the root of the repository, cd into the finite-element scripts directory and run with FreeFEM via the commandline:

cd freefem/release/report-1
FreeFem++ solve-Efield.edp # for the primary simulation
FreeFem++ solve-Efield-validation.edp # for the validation simulation

For the finite-difference simulations, from the root of the repository, cd into the notebook directory and start Jupyter notebook for interactive programming with the given notebook:

cd notebooks/archived
jupyter notebook