Sorbonne Université

High Performance in Scientific Computing

Course coordinator : Frédéric Nataf

The High Performance in Scientific Computing Major (HPC) is one of the Majors available in the Mathematical Modelling Masters degree programme, which is the second year of the Mathematics and Applications Master.

High Performance Computing plays a major role in scientific research and industrial innovation. The architecture of large scale computers is evolving rapidly and is becoming more and more complex. These computers are formed by heterogeneous units and the number of computing cores exceeds the million. This exaflop computing capability opens new possibilities for scientific computing, 1but requires new algorithms and a deep understanding of both computer structures and mathematical modelling.

These areas of research are currently blooming, with many advances required in order to efficiently exploit current and upcoming parallel computers. However, the required skills are still not available on the market, both in the research field and in academic training courses. This is also the case for the research and development divisions of major industry groups that have the necessary teams to work in this field. They also base their competitiveness not only on better management and optimisation, but also on a deeper understanding of their products through the use of mathematical modelling. Every single high tech industry is involved, from banks to organisations fosusing on society-relevant issues (global warming, pollution, management).

The HPC Major courses cover the following topics:

• Advanced methods for the numerical resolution of partial differential equations arising from physics, chemistry, graph theory.
• Introduction to parallel computing with an overview of parallel machines, programming languages, practical parallel coding.
• Design of efficient parallel algorithms using e.g. parallelism in space and time, communication avoiding techniques.
• Parallel computing aspects arising in the analysis of large data sets, going from matrices to tensors in high dimension.