Postdoctoral research associate (independent), Numerical Analysis group, Oxford Mathematical Institute.Research interests:
The finite element method for the PDEs of elasticity and thermodynamics, encompassing:
- Piola transformation theory and implementation of FEM
- Elasticity complexes and the discretisation of elastic stress and strain
- Multigrid, preconditioning, and fast solvers
Preprints:Aznaran, F. R. A., Farrell, P. E., Monroe, C. W., and Van-Brunt, A. J., Finite element methods for multicomponent convection-diffusion, Aug. 2022, arXiv:2208.11949 [bib, pdf]
Publications:Aznaran, F. R. A., Kirby, R. C., and Farrell, P. E., Transformations for Piola-mapped elements, SMAI Journal of Computational Mathematics (to appear), 2023, arXiv:2110.13224 [bib, pdf]
- 2022–present: EPSRC Postdoctoral Research Associate, Mathematical Institute, University of Oxford.
- 2018–2022: DPhil candidate in Numerical Analysis/OxPDE (via the EPSRC CDT in PDEs), The Queen's College, University of Oxford.
- Thesis: Discretisation of Hodge Laplacians in the elasticity complex.
- 2017–18: MASt Applied Mathematics (Part III), Corpus Christi College, University of Cambridge.
- Essay: Highly oscillatory quadrature.
- 2014–17: BSc Mathematics, University of Warwick.
Combined EPSRC/MathWorks Scholarship at the PDEs CDT, Oxford Mathematical Institute (2018–22).
- ICIAM 2023 minisymposium: Finite element complexes for structure-preservation in continuum mechanics.
- Summer project available: Nonlinear elasticity and Newton's method in infinite dimensions, with Dr Charles Parker, for 3rd/4th year undergraduates at Oxford.
- Oxford FEM reading group.
- SIAM Annual Meeting 2022 minisymposium: Nonlinear viscous flow: Numerical methods and applications. MS30 Part I, MS57 Part II, MS85 Part III.
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK