AI-based Materials and Process Simulation I
Course materials · finite elements with FEniCSx (DOLFINx 0.11) on Google Colab
Start here
- Read the syllabus (PDF): schedule, grading, AI policy, academic integrity.
- Click a notebook link (lab, assignment): it opens in Google Colab. First File → Save a copy in Drive — the copy in your Drive is the one you work on and submit. Run its first cell (setup, 3–5 min once per runtime). Cells marked
%%fenicsx -np Nrun DOLFINx 0.11 with N MPI processes. - Before every submission: Runtime → Restart session and run all, check every output, fill in the AI-usage log (Markdown).
References: DOLFINx 0.11 API sheet (also give it to your LLM assistant) · project topics · final project guide
Weekly materials
Each week: slides (in class), a lab notebook (in class), the assignment (due before the next lecture), and a README with the details. Each lecture opens with a 10-minute closed-AI quiz on the previous week; Week 8 opens with the midterm exam.
| Week | Topic | Slides | Lab | Assignment / notebook | Overview |
|---|---|---|---|---|---|
| 1 | Poisson’s Equation, Numerical Quadrature, First DOLFINx Solver | slides | lab | HW0 HW1 |
README |
| 2 | Ciarlet’s Finite Element, Unisolvence, Basix Elements, Lagrange Variants | slides | lab | HW2 | README |
| 3 | From Local Elements to a Global Space: Continuity, DG Spaces, Mesh Topology, the DOF Map | slides | lab | HW3 | README |
| 4 | Interpolation Operators, Sobolev Norms, Scaling; Functions, Interpolation and Errors in DOLFINx | slides | lab | HW4 | README |
| 5 | Hilbert Spaces, Riesz Representation, Lax–Milgram; Assembly, PETSc KSP and the Method of Manufactured Solutions | slides | lab | HW5 | README |
| 6 | Boundary Conditions: Mean Estimate, Pure Neumann, Trace Inequality, Partial Dirichlet, Robin; Dirichlet Lifting, Subdomains and Gmsh | slides | lab | HW6 | README |
| 7 | Weak Derivatives and Sobolev Spaces, Céa’s Lemma, Elliptic Regularity, Aubin–Nitsche; Computing Convergence Rates Correctly | slides | lab | HW7 | README |
| 8 | Midterm · Nonlinear Problems I: Residual Form, Gâteaux Derivative, Newton’s Method by Hand · Project Proposal | slides | lab | project proposal | README |
| 9 | Nonlinear Problems II: Well-posedness · Globalisation · Continuation · PETSc SNES in DOLFINx | slides | lab | HW8 | README |
| 10 | Time-Dependent Problems: θ-Method · Stability · Space–Time Convergence · Cahn–Hilliard | slides | lab | HW9 | README |
| 11 | Stokes Flow: Mixed Problems · Inf-Sup · Brezzi · Taylor–Hood, MINI and Unstable Pairs | slides | lab | HW10 | README |
| 12 | Solving Saddle-Point Systems: Schur Complement · Block Preconditioners · fieldsplit · Stokes and Darcy | slides | lab | HW11 | README |
| 13 | Advection–Diffusion: Péclet Number · Galerkin Oscillations · Upwinding · SUPG | slides | lab | HW12 | README |
| 14 | Navier–Stokes: Projection Methods (Chorin, IPCS) · CFL · Channel Flow · DFG 2D-3 | slides | lab | HW13 | README |
| 15 | Steady Navier–Stokes: Newton · Reynolds-Number Continuation · Lid-Driven Cavity · PCD · H(div)-Conforming DG | slides | lab | HW14 | README |
| 16 | Final Project Presentations | guide | – | render report report template |
README |