101-0250-00L  Solving Partial Differential Equations in Parallel on GPUs

Courses

Catalogue data

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.
Learning 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).
Lecture notes	Digital lecture notes, interactive Julia notebooks, online material.
Literature	Links to relevant literature will be provided during classes.
Prerequisites / Notice	Completed BSc studies. Interest in and basic knowledge of numerics, applied mathematics, and physics/engineering sciences. Basic programming skills (in e.g. Matlab, Python, Julia); advanced programming skills are a plus.
Competencies	Subject-specific Competencies Concepts and Theories assessed Techniques and Technologies assessed Method-specific Competencies Analytical Competencies assessed Decision-making assessed Media and Digital Technologies assessed Problem-solving assessed Project Management assessed Social Competencies Communication fostered Cooperation and Teamwork fostered Personal Competencies Creative Thinking assessed Critical Thinking assessed

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits	4 credits
Examiners	L. Räss, S. Omlin, M. Werder
Type	graded semester performance
Language of examination	English
Repetition	Repetition only possible after re-enrolling for the course unit.
Additional information on mode of examination	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.

Learning materials

Groups

Restrictions

Offered in

Programme	Section	Type
Civil Engineering Master	Major in Hydraulic Engineering and Water Resources Management	W
Civil Engineering Master	Digitalisation Specific Courses	W
Civil Engineering Master	Project Based Courses	W
Computer Science Bachelor	Minor Courses	W
Computational Science and Engineering Master	Electives	W