Tutorials

These tutorials are structured as a software-demo book. Each chapter starts from a runnable script in python/demo, explains the mathematical problem, then follows the CutFEMx workflow used in the code.

The embedded panels are PyVista screenshots generated from the same DOLFINx meshes and CutFEMx classification steps as the demo scripts. Each chapter uses several focused panels so the geometry being discussed is visible next to the corresponding code and equations.

Tutorial Book

• Cut Poisson
• DG Poisson
• Interface Poisson
• Surface Poisson DG
• Stokes Flow
• Exterior-Facet Runtime Quadrature
• STL Distance
• Elasticity
• Moving Poisson
• Tutorial Visualizations

Suggested Session Flow

1. Start with Cut Poisson to introduce level sets, entity classification, runtime quadrature, and inactive-DOF deactivation.

2. Move to DG Poisson to show why interior facets also need cut quadrature.

3. Use Interface Poisson to show two cut phases coupled across one unfitted interface.

4. Use Surface Poisson DG to demonstrate integration directly on \(\phi=0\).

5. Use Stokes and Elasticity to show mixed and vector-valued problems.

6. Use Exterior-Facet Runtime Quadrature for codimension-two quadrature on boundary facets.

7. Use STL Distance to see how STL geometry becomes a level-set field.

8. Finish with Moving Poisson to show the same background mesh with rebuilt cut data over several geometry positions.