Supplementary material to "Numerical efficiency of explicit time integrators for phase-field models"

The supplementary material complements the paper with the following:

• Complete data for the small scale benchmarks, together with notebooks detailing the analysis.
• Processed data and a notebook for the 3D benchmarks.
• Additional graphs based on the data which didn't make it into the paper.
• Videos of the 3D microstructural evolution.
• Derivation of the parameter relationships & maximal eigenvalue estimates.
• Details of a noise-resistant convergence testing algorithm & derivation of an O(W^2) error in the phase-field volume.

The videos include immobile.webm, in which the a grain structure undergoes coarsening by mean curvature flow and contains immobile particles which eventually realize a limiting grain size; mobile.webm which contains mobile particles (pores) which move together with the grain boundaries and merge, which is shown in detail for a region within merge.webm. For immobile particles, only the grain boundaries are visualized. For mobile particles, only the triple phase lines (dark) together with pores (transparent blue) are visualized.

The notebooks are provided as static PDFs for ease of viewing as well as interactive Jupyter notebooks. The latter requires several python packages, which are most easily installed in a fresh virtual environment with `pip install -r requirements.txt`. Using uv as a Python package manage might speed up that installation significantly. A nbclassic Jupyter environment is assumed, as part of the requirements; if you prefer jupyterlab, adjust the %matplotlib magic at the top of the notebooks.