AMPS I · Week 09 — Nonlinear Problems II: Well-posedness · Globalisation · Continuation · PETSc SNES in DOLFINx

File What When
W09_lecture.html (.qmd source) Lecture slides — Parts A (theory), B (SNES), C (continuation, Bratu), D (LLM, HW8) in class
W09_lab.ipynb (Colab) Lab: NonlinearProblem and its diagnostics, a silent failure, line search vs initial guess, continuation in the data, Bratu’s fold, a custom Newton solver that passes it, LLM demo in class (≈ 70 min), finish at home
W09_HW8.ipynb (Colab) HW8 — Kirchhoff transform and the exact 1D Bratu problem; -\nabla\cdot(e^u\nabla u)=f with SNES (MMS, Kirchhoff cross-check, stopping tolerance); 1D Bratu fold vs the exact \lambda^*; LLM debugging due before Week 10
../dolfinx_0.11_api_reference.md DOLFINx 0.11 API reference sheet — paste it into your LLM always

The session starts with a 10-minute quiz on the Week 8 lecture (closed-AI). Proposal feedback is handed back in class.

HW8 Q3 reuses bratu_branch and fold from lab §4 — run the lab first.

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, and a failed SNES solve does not raise an error either — print the converged reason after every solve() and read every output before you submit.

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