PhD Studentship: Mixed precision methods for numerical linear algebra at exascale

Number of Positions: 1

Eligibility: UK Only

Funding: School of Computer Science Scholarship, in support of the EPSRC Grant: Mixed precision in Krylov Methods, providing the award of full academic fees, together with a tax-free maintenance grant at the standard UKRI rate of £20,780 per year for 3.5 years. 

Lead Supervisor’s full name & email address

Dr Massimiliano Fasi: m.fasi@leeds.ac.uk

Project summary

Join an international team developing scalable algorithms to solve numerical linear algebra challenges on supercomputers.

Modern high-performance computing increasingly relies on hardware accelerators originally designed for artificial intelligence. These accelerators achieve exceptional performance by using low precision arithmetic, which is sufficient for machine learning tasks but much too inaccurate for most scientific applications. To harness these accelerators for scientific computing, one must develop new algorithms that combine low and high precision computations in a way that preserves accuracy while delivering significant gains in terms of speed and energy efficiency.

This PhD project will focus on developing mixed-precision algorithms for large-scale, sparse eigenvalue problems and matrix functions. These computational problems are central to many scientific and engineering applications, including quantum mechanics, materials science, and weather/climate modelling. Numerical methods currently available cannot fully exploit modern accelerators, and are therefore not suitable to run on today’s largest supercomputers. By redesigning these algorithms for mixed-precision, the project aims to deliver robust, scalable solutions that will eventually be integrated into widely used scientific software libraries.

The successful candidate will join a dynamic research environment and gain access to state-of-the-art supercomputers. There will be opportunities to collaborate with researchers at the University of Leeds, the Rutherford Appleton Laboratory, a UK National Lab in Oxfordshire, and Environment and Climate Change Canada, the Canadian counterpart of the Met Office. The algorithms developed during the PhD will become part of SLEPc (the Scalable Library for Eigenvalue Problem Computations, hosted at the Universitat Politècnica de València) and SLATE (Software for Linear Algebra Targeting Exascale, hosted at the University of Tennessee at Knoxville).

By the end of the PhD, the student will have gained knowledge and experience in numerical analysis, with a particular focus on linear algebra, and in high performance computing. There will be opportunities to present research at national and international conferences, work on scientific publication, and contribute to widely used scientific software libraries.

Please state your entry requirements plus any necessary or desired background

A first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline.

Applicants should have a strong interest in numerical algorithms and scientific computing. A background in applied mathematics, computational mathematics, computer science, physics, or engineering is suitable. Basic programming experience (e.g., C, C++, Julia, MATLAB, Python, or similar) is necessary; knowledge of numerical linear algebra or high performance computing is desirable, however, training will be provided. 

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