I undertook my undergraduate studies at the National University of Ireland, Galway (2006) and my doctoral studies at Imperial College London (2010).
After working as a postdoctoral researcher at Imperial, I won an EPSRC Early Career Research Fellowship and moved to the Mathematical Institute and Christ Church, Oxford (2013). In 2015 I won the quadrennial Wilkinson Prize for Numerical Software and an IMA Leslie Fox Prize in Numerical Analysis.
My research lies at the junction of mathematics, physics, engineering, and computation. In my thesis and early postdoctoral work, my research focussed on adaptive mesh discretisations: changing the computational mesh in some way to make orders of magnitude efficiency gains in solving complex models. In this work, I solved a problem of computational geometry that had been open in the literature for over twenty years.
In my later postdoctoral work, I have focussed on the problem of automatically deriving adjoint models. Adjoints are absolutely essential for many important problems, such as weather prediction, optimising the shape of wings, and quantifying the accuracy of nuclear simulations. I have developed an entirely new approach to deriving adjoint models, which yields dramatic gains in automation, robustness and efficiency - in some cases, from years to days. With these methods in hand, it is now possible to contemplate the automated solution of optimisation problems constrained by the laws of physics. Such applications are of huge interest and importance across all of engineering and the quantitative sciences.
A. G. Buchan, P. E. Farrell, G. J. Gorman, A. J. H. Goddard, M. D. Eaton, E. T. Nygaard, P. L. Angelo, R. P. Smedley-Stevenson, S. R. Merton, and P. N. Smith (2014). "The immersed body supermeshing method for modelling reactor physics problems with complex internal structures". In: Annals of Nuclear Energy 63.0, pp. 399–408. doi:10.1016/j.anucene.2013.07.044
S. W. Funke, P. E. Farrell, and M. D. Piggott (2013). Tidal turbine array optimisation using the adjoint approach. Accepted in Renewable Energy. arXiv:1304.1768 [math.OC]
P. E. Farrell, C. J. Cotter, and S. W. Funke (2013). A framework for the automation of generalised stability theory. Accepted in SIAM Journal on Scientific Computing. arXiv:1211.6989 [cs.MS]
P. E. Farrell, D. A. Ham, S. W. Funke, and M. E. Rognes (2013). “Automated derivation of the adjoint of high-level transient finite element programs”. In: SIAM Journal on Scientific Computing 35.4, pp. C369–C393. doi:10.1137/120873558
J. Southern, G.J. Gorman, M.D. Piggott, and P. E. Farrell (2012). “Parallel anisotropic mesh adaptivity with dynamic load balancing for cardiac electrophysiology”. In: Journal of Computational Science 3.1–2, pp. 8–16. doi:10.1016/j.jocs.2011.11.002
P. E. Farrell (2011). “The addition of fields on different meshes”. In: Journal of Computational Physics 230.9, pp. 3265–3269. doi: 10.1016/j.jcp.2011.01.028
P. E. Farrell and J. R. Maddison (2011). “Conservative interpolation between volume meshes by local Galerkin projection”. In: Computer Methods in Applied Mechanics and Engineering 200.1-4, pp. 89–100. doi: 10.1016/j.cma.2010.07.015
P. E. Farrell, S. Micheletti, and S. Perotto (2011). “An anisotropic Zienkiewicz-Zhu error estimator for 3D applications”. In: International Journal for Numerical Methods in Engineering 85.6, pp. 671–692. doi: 10.1002/nme.2980
P. E. Farrell, M. D. Piggott, C. C. Pain, G. J Gorman, and C. R. G. Wilson (2009). “Conservative interpolation between unstructured meshes via supermesh construction”. In: Computer Methods in Applied Mechanics and Engineering 198.33-36, pp. 2632–2642. doi: 10.1016/j.cma.2009.03.004