AMPS I · Week 06 — Boundary Conditions: Mean Estimate, Pure Neumann, Trace Inequality, Partial Dirichlet, Robin; Dirichlet Lifting, Subdomains and Gmsh

File What When
W06_lecture.html (.qmd source) Lecture slides — Parts A, B, C, D in class
W06_lab.ipynb (Colab) In-class lab: mean-estimate, trace and partial-Dirichlet constants, a Dirichlet condition by hand, MMS with Dirichlet + Neumann + Robin conditions, pure Neumann with a PETSc nullspace, a two-material Gmsh mesh, LLM demo in class (≈ 80 min)
W06_HW6.ipynb (Colab) HW6 — proofs (pure Neumann, Robin, lifting), a composite wall with a convective boundary, coercivity constants for Robin and for one pinned DOF, an LLM-generated mixed-BC solver with planted bugs due before Week 7
../dolfinx_0.11_api_reference.md DOLFINx 0.11 API reference sheet (§7 LinearProblem, §8 manual assembly + KSP, §11 parallel-safe norms) — paste it into your LLM always

Open a notebook in Colab: click its link on the course page or below — it opens in Colab; then File → Save a copy in Drive and work on that copy. (Or upload the .ipynb to Google Drive → right-click → Open with → Google Colaboratory.) Run the setup cell first (≈ 3–5 min); re-run it after every runtime restart.

Where code can run: basix, ufl, dolfinx, petsc4py, gmsh (and SciPy for the small dense eigenvalue problems) are used only inside %%fenicsx cells. Ordinary cells have NumPy and matplotlib only.

Before submitting: Runtime → Restart session and run all, fill in the AI-usage log, download the .ipynb. An error inside a %%fenicsx cell does not stop Run all: the traceback is printed and the next cell runs anyway. Scroll through every output before you submit. A cell that printed a traceback, and any plot that uses its results, earns no points. (The first cell of HW6 Q4 is meant to fail — it is marked EXPECTED-FAIL.)

Week 7 starts with a 10-minute quiz on this week’s material (closed-AI).