Professor Patrick Farrell undertook his undergraduate studies at the National University of Ireland, Galway (2006) and his doctoral studies at Imperial College London (2010).
After working as a postdoctoral researcher at Imperial, he won an EPSRC Early Career Research Fellowship and moved to the Mathematical Institute and Christ Church, Oxford (2013). In 2015 he won the quadrennial Wilkinson Prize for Numerical Software and an IMA Leslie Fox Prize in Numerical Analysis.
Research Interests
Professor Farrell’s research interests centre on the numerical solution of partial differential equations arising in physics and chemistry. The goals of his research are to extend humanity’s numerical simulation capabilities, to develop new numerical algorithms that are useful to science and important to society, and to collaborate with scientists and engineers to translate numerical solutions into scientific advances.
He particularly focuses on the development of structure-preserving finite element discretisations in space and time, adjoint techniques and their applications, bifurcation analysis of nonlinear problems, and preconditioners and fast solvers.
He has applied the numerical techniques he develops to applications in the areas of renewable energy, cardiac electrophysiology, glaciology, magnetohydrodynamics, quantum mechanics, liquid crystals, and multicomponent flows.
Selected Publications
- 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
- 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
- E. Farrell, Á. Birkisson, and S. W. Funke (2015). “Deflation techniques for finding distinct solutions of nonlinear partial differential equations”. In: SIAM Journal on Scientific Computing 37.4, A2026– A2045. doi: 10.1137/140984798
- E. Farrell, M. Croci, and T. M. Surowiec (2019). “Deflation for semismooth equations”. In: Opti- mization Methods and Software 35.6, pp. 1248–1271. doi: 10.1080/10556788.2019.1613655
- E. Farrell, L. Mitchell, and F. Wechsung (2019). “An augmented Lagrangian preconditioner for the 3D stationary incompressible Navier–Stokes equations at high Reynolds number”. In: SIAM Journal on Scientific Computing 41.5, A3073–A3096. doi: 10.1137/18M1219370