Francis Aznaran

Postdoctoral research associate (independent), Numerical Analysis group, Oxford Mathematical Institute.

Currently on a research visit to Baylor University, Texas.

Research interests:
The finite element method for the PDEs of elasticity and thermodynamics, encompassing:

• Piola transformation theory and implementation of finite element bases
• Elasticity complexes and the discretisation of elastic stress and strain
• Multicomponent fluid flows
• 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]

Brief CV:

• 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.

Awards:
Combined EPSRC/MathWorks Scholarship at the PDEs CDT, Oxford Mathematical Institute (2018–22).

Further information:

• 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 3^rd/4^th 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.

Contact:
aznaran@maths.ox.ac.uk
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK