Patrick E. Farrell is a Professor in the Numerical Analysis group of the University of Oxford and a Tutorial Fellow at Oriel College, Oxford. He works on the numerical solution of partial differential equations, focusing on finite element methods, bifurcation analysis of nonlinear PDE, adjoint techniques, their application and automation, preconditioners, and fast solvers. The London Mathematical Society and Society for Industrial and Applied Mathematics have awarded Farrell.

We had the opportunity to interview Patrick E. Farrell, one of the plenary speakers at the HPCSE 2024 conference, organised by IT4Innovations National Supercomputing Center.

Your studies and career have been filled with mathematics. Can you remember when mathematics, followed by computational physics, fascinated you so much that you decided to pursue it in your studies and career?

Farrell: I was sure that I wanted to study mathematics from about the age of 15, after reading Fermat's Last Theorem by Simon Singh. It's now a great honour to me that I work in the same department as Andrew Wiles, the star of the book!

Do you use supercomputers in your work? Which ones?

Farrell: I use the UK national supercomputer, ARCHER2. I also occasionally use the Oxford local supercomputing service, and Isambard.

At the HPCSE 2024 conference, you presented on "Reynolds-robust solvers for incompressible flow problems." For those unable to attend, could you explain the focus and significance of your research in this area?

Farrell: Solving linear systems like Ax = b is a central task in numerical simulation. Direct methods, like sparse LU factorisations, do not scale to very large problems, so preconditioned iterative methods like GMRES are typically used on supercomputers. A key property you want from a preconditioner is parameter-robustness: that the number of GMRES iterations does not vary too much as you vary problem parameters. My talk described a specialised preconditioner for the incompressible Navier-Stokes equations that displays remarkable robustness with respect to varying the Reynolds number.

Among the various applications of your numerical techniques in renewable energy, cardiac electrophysiology, glaciology, magnetohydrodynamics, quantum mechanics, and liquid crystals, which recent success are you most proud of and why?

Farrell: Scientifically, I will mention two: developing a new theory for smectic liquid crystals, which reproduced various experimental phenomena from a single energy functional, and discovering new solutions of Bose-Einstein condendates in quantum mechanics. Personally, one of the most rewarding was my work in inverse problems in glaciology, which gave me the opportunity to undertake fieldwork with the British Antarctic Survey, flying to remote glaciers and skiing across them to collect the data.

Has any particular research from the other speakers at the HPCSE 2024 caught your attention?

Farrell: The standard of talks was very high. I greatly enjoyed the talks on developments in finite element software and domain decomposition solvers, as these are close to my research area. I was struck by the remarkable beauty of the visualisations described by Guillermo Marin. I also greatly enjoyed the talk on specialised interior point algorithms by Jacek Gondzio.

You have visited the Czech Republic several times on business; what do you think of the HPCSE 2024 venue and the conference itself?

Farrell: The venue is fabulous: beautiful views, comfortable rooms, wonderful food, an excellent lecture theatre, and even better company. I strongly recommend it.