🎉 Welcome to Part II of Solving PDEs in Parallel on GPUs. In this course, you will work in teams of two to design, implement, optimise, and run a complete high-performance numerical application on modern heterogeneous supercomputers.
The focus of the course is on developing a scientific computing application from start to finish, including mathematical model formulation, discretisation and algorithm design, GPU implementation in Julia, performance optimisation, execution on a supercomputer, validation and performance analysis.
By the end of the semester, you will be able to independently develop and assess a non-trivial GPU-accelerated solver and understand its numerical and computational behaviour at scale.
During the semester you will:
Form a team of two (contact the instructors if you need help finding a teammate).
Select a project topic (from the list below or propose your own).
Send a short project proposal by email, including a brief description of the problem, a preliminary work plan, and up to three key literature references.
Present your project proposal, 10 minutes total: 7 minutes talk + 3 minutes discussion.
Develop a working prototype.
Present a progress report, including demonstration of the prototype, preliminary numerical results, issues encountered, potential changes to the plan.
Continue development and optimisation.
Present the final project, including validated numerical results, performance benchmarks, scalability discussion reflection on challenges and lessons learned, possible future extensions.
Finalise and polish the repository.
Submit the project by providing the SHA of the final commit on Moodle.
(Optional) Submit an entry for the course gallery with a short description and a figure or animation.
Presentations must be uploaded to Moodle before the presentation day.
Instructors will be available in person either biweekly in the office or upon request.
All communication takes place on Element.
Code must be hosted on GitHub.
Access to the computing infrastructure will be provided later shortly after the first presentation.
De-registration from the course is only possible before the project deadline selection deadline (see below). Students who won't deregister will be graded by the end of the semester.
24.02.2026 — Project topic selection deadline
03.03.2026 — Proposal presentation
31.03.2026 — Progress presentation
12.05.2026 — Final presentation
29.05.2026 — Project submission deadline
Each topic is structured in tiers of increasing complexity. Higher tiers correspond to more challenging features and typically contribute toward higher grades. The list in non-exhaustive, and you are encouraged to come up with your own topic based on your research interests.
1. Turbulence – Navier–Stokes Solver
2D incompressible solver
3D solver
Internal boundaries or obstacles
Smoke / passive scalar simulation
Efficient Poisson solver (Krylov / Multigrid / FFT)
2. Ice Sheet Modelling – Depth-Averaged Ice Flow
SIA (Shallow Ice Approximation)
SSA (Shallow Shelf Approximation)
DIVA or hybrid models
3. Ocean and Atmosphere Modelling – Shallow Water Equations
Cartesian coordinates
Barotropic instabilities
Internal boundaries
Spherical coordinates
4. Electromagnetic Wave Propagation – Maxwell Solver
2D formulation
3D formulation
Perfectly Matched Layers (PML)
5. Mantle Convection – Thermomechanically Coupled Stokes Solver
2D formulation
3D formulation
Spherical geometry
6. CO₂ Storage and Porosity Waves – Coupled Porous Flow
2D model
3D model
Coupling with Stokes flow
7. Phase Separation – Cahn–Hilliard Solver
2D implementation
3D implementation
Implicit/dual-time time stepping
Passing (4.0–5.0)
All presentations delivered
Project repository submitted
Working code
Numerical results and figures
Basic README
Good (5.0–5.5)
Clear code documentation
Unit tests
Continuous integration (CI)
GPU implementation
Performance benchmarks
Meaningful results
Animations
Excellent (5.5–6.0)
Multi-GPU implementation
Scalability study
Numerical validation against references
Advanced or difficult extensions
Clear scientific and performance analysis
There are no restrictions on using AI tools (e.g., for code generation, debugging, documentation, or literature search).
However:
You are fully responsible for your code and results.
"Vibe-coding" without understanding the implementation is strongly discouraged.
Your repository must include a section in the README specifying which AI tools were used, for which tasks, and how they contributed to the project.
