Solving Partial Differential Equations in Parallel on GPUs II

Abstract

This course builds on 101-0250-00 Solving Partial Differential Equations in Parallel on GPUs I and focuses on the design, implementation, and execution of a complete high-performance numerical application on modern supercomputing systems.

Objective

Modern scientific computing increasingly relies on large-scale simulations executed on heterogeneous supercomputers combining CPUs and GPUs. The objective of this course is to guide students through the full lifecycle of a high-performance numerical application: from mathematical model formulation and algorithm design to GPU implementation, optimisation, and execution on a supercomputer. Students will work in teams of two to design and implement a GPU-accelerated PDE solver in Julia, targeting a realistic scientific or engineering problem. Emphasis is placed on memory efficiency, parallel scalability, and following the best practices in scientific software engineering. By the end of the course, students will be able to independently develop, analyse, and run a non-trivial GPU-based numerical code on a supercomputing system, and critically assess its numerical accuracy and performance.

Content

Part 1 – Project definition and numerical modelling - Selection and formulation of a PDE-based physical or engineering problem; - Choice of numerical discretisation and time-integration strategy; - Presentation of the project. Part 2 – GPU implementation and performance optimisation - Implementation of GPU kernels in Julia; - Memory-aware algorithm design and optimisation; - Identification and mitigation of performance bottlenecks; - Progress report. Part 3 – Multi-GPU execution and supercomputing workflows - Execution on a supercomputer (job scheduling, scaling tests); - Performance analysis and validation of numerical results; - Documentation and presentation of the final project.

Resources