Front page

I am an EPSRC Early Career Research Fellow in the Numerical Analysis group of the University of Oxford, with appointments as a Postdoctoral Research Fellow at Christ Church, Oxford and as an Adjunct Research Scientist at Simula Research Laboratory, Oslo. I work on the numerical solution of partial differential equations, with a particular focus on adaptive techniques that can exploit anisotropy, the automated derivation of adjoint models, and the computation of multiple solutions of PDE-constrained optimisation problems. I’m fascinated by many topics in computational mathematics, including linear and nonlinear preconditioning, solvers for difficult nonlinear equations, structure-preserving discretisations, continuation and bifurcation analysis, and complementarity problems. I apply the numerical techniques I develop to various applications, including tidal turbines for renewable energy, bidomain cardiac electrophysiology, radiation transport, and glaciology.

I mainly code in Python, contribute regularly to the FEniCS and PETSc
software projects, and lead the development of dolfin-adjoint.

News

2016-03-16: A new paper is up on arXiv about optimal preconditioners for the Ohta–Kawasaki equations with John Pearson.

2016-03-15: There’s an open faculty position in numerical analysis in Oxford (an associate professorship). Apply by April 29!

2016-03-03: A new paper is up on arXiv about computing disconnected bifurcation diagrams with deflation with Casper Beentjes and Ásgeir Birkisson.

2016-01-28: A new paper is up on arXiv about using deflation to compute multiple equilibria of nematic liquid crystals with James Adler, David Emerson and Scott MacLachlan.

2015-11-30: Another paper is up on arXiv about linear and nonlinear solvers in variational fracture mechanics with Corrado Maurini. The code that supports the manuscript is available on bitbucket.

2015-10-09: A new paper with my MSc student Matteo Croci is up on arXiv about multiple solutions of complementarity problems via deflation. The code that supports the manuscript is available on bitbucket.

2015-09-19: Images from the SIAM Awards Lunch in Beijing are online.

2015-09-18: I gave the invited scientific lecture to the annual general meeting of NAG.

2015-09-01: A new paper is up on arXiv about PDE-constrained optimisation, deflation and Schur complement preconditioners.

2015-08-31: I’ve just released a Python implementation of Mike Giles’ multilevel Monte Carlo demo code.

2015-08-27: The first deflation paper has been published online in SISC.

2015-08-13: I collected the Wilkinson prize at ICIAM 2015 in Beijing today. Thanks again to NAG, ANL and NPL.

2015-07-16: I have been selected for polar service with the British Antarctic Survey! I will be undertaking fieldwork in the Antarctic this November as part of an observational campaign on the retreating ice sheets on the east coast of the Antarctic peninsula, on Flask Glacier and Scar Inlet.

2015-06-23: I came second in the Fox prize competition, joining company such as Andy Wathen, Peter Sweby, Alan Edelman, Mark Ainsworth, Barry Smith, and Des Higham. Congratulations to Iain Smears and Alex Townsend.

2015-06-11: I have won the 2015 Wilkinson prize for Numerical Software, along with my colleagues Simon Funke, David Ham and Marie Rognes.

2015-03-06: I have been shortlisted for the 17th IMA Leslie Fox prize in numerical analysis.

Contact

Email: patrick.farrell@maths.ox.ac.uk
Phone: +44 1865 270743
Post: S2.34 Mathematical Institute
Radcliffe Observatory Quarter
University of Oxford
Oxford
UK OX2 6GG