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101-0250-00L 4 Credits BSC , MSC D-MATH , D-BAUG , D-INFK
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Solving Partial Differential Equations in Parallel on GPUs

Lecturers & Examiners: Dr. Mauro Werder, Dr. Ludovic Räss, Dr. Samuel Omlin
VVZ CR 3.2

Last Updated: 2026-02-05 16:01:14

Abstract

This course aims to cover state-of-the-art methods in modern parallel Graphical Processing Unit (GPU) computing, supercomputing and code development with applications to natural sciences and engineering.

Objective

When quantitative assessment of physical processes governing natural and engineered systems relies on numerically solving differential equations, fast and accurate solutions require performant algorithms leveraging parallel hardware. The goal of this course is to offer a practical approach to solve systems of differential equations in parallel on GPUs using the Julia language. Julia combines high-level language conciseness to low-level language performance which enables efficient code development. The course will be taught in a hands-on fashion, putting emphasis on you writing code and completing exercises; lecturing will be kept at a minimum. In a final project you will solve a solid mechanics or fluid dynamics problem of your interest, such as the shallow water equation, the shallow ice equation, acoustic wave propagation, nonlinear diffusion, viscous flow, elastic deformation, viscous or elastic poromechanics, frictional heating, and more. Your Julia GPU application will be hosted on a git-platform and implement modern software development practices.

Content

Part 1 - Discovering a modern parallel computing ecosystem - Learn the basics of the Julia language; - Learn about the diffusion process and how to solve it; - Understand the practical challenges of parallel and distributed computing: (multi-)GPUs, multi-core CPUs; - Learn about software development tools: git, version control, continuous integration (CI), unit tests. Part 2 - Developing your own parallel algorithms - Implement wave propagation and porous convection; - Apply spatial and temporal discretisation (finite-differences, various time-stepper); - Implement efficient iterative algorithms; - Implement shared (on CPU and GPU) and distributed memory parallelisation (multi-GPUs/CPUs); - Learn about main simulation performance limiters. Part 3 - Final project - Apply your new skills in a final project; - Implement advanced physical processes (solid and fluid dynamic - elastic and viscous solutions).

Resources

Lecture Notes

Digital lecture notes, interactive Julia notebooks, online material.

Literature

Links to relevant literature will be provided during classes.

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
graded semester performance
The graded semester performance consists of: (1) 5 (out of 6) weekly assignments (30% of the final grade) during the course’s Parts 1; (2) a project during Part 2 (35% of the final grade); (3) a final project during Part 3 (35% of the final grade). (1) Weekly coding exercises can be done alone or in groups of two. (2) Projects and (3) final projects are to be worked on alone or in groups of two and submission includes codes in a git repository and (an automatic generated) documentation as report.The course being an advanced Master course, students are expected to work independently and manage the workload accordingly.

Registration & Places

Max Places
25

Course Components

Type Title Time & Place Hours
lecture with exercise Solving Partial Differential Equations in Parallel on GPUs
  • Tue 12:45-15:30 (HCI E 8)
3 h weekly

Offered In