Francis Aznaran

BSc (Warwick), MASt (Cantab), DPhil (Oxon)

Status

Postdoctoral Research Associate

https://aznaran.com

+44 1865 615121

ORCID iD

https://orcid.org/0000-0001-9843-9852

Research groups

Numerical Analysis

Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Prizes, awards, and scholarships

Combined EPSRC/MathWorks Scholarship at the PDEs CDT, Oxford Mathematics Institute (2018–2022).

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

Further details

ICIAM 2023 minisymposium: Finite element complexes for structure-preservation in continuum mechanics.

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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.

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Oxford FEM reading group.

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SIAM Annual Meeting 2022 minisymposium: Nonlinear Viscous Flow: Numerical Methods and Applications, MS30 Part I, MS57 Part II, MS85 Part III.

Major / recent publications

Finite element methods for multicomponent convection-diffusion, F. R. A. Aznaran, P. E. Farrell, C. W. Monroe, and A. J. Van-Brunt, submitted, Aug. 2022 (arXiv:2208.11949).
Transformations for Piola-mapped elements, F. R. A. Aznaran, P. E. Farrell, and R. C. Kirby, SMAI Journal of Computational Mathematics (to appear), 2023 (arXiv:2110.13224).

Teaching

Hilary '23: Tutor, Part C Finite Element Methods for PDEs.
Michaelmas '22: Tutor, Part B Functional Analysis I.
Hilary '22: Tutor, Part C Fixed Point Methods for Nonlinear PDEs.
Michaelmas '21: Tutor, MMSC Numerical Solution of PDEs.
Hilary '21: Tutor, Part B Functional Analysis II; TA, Part C Finite Element Methods for PDEs.
Michaelmas '20: TA, Part C Functional Analytic Methods for PDEs; TA, MMSC Numerical Solution of Differential Equations I.
Nov '20: Marker, Oxford MAT.
Hilary '20: TA, Part B Functional Analysis II.
Michaelmas '19 - Trinity '20: Tutor of Prelims Introductory Calculus, and marker of Collections, Oriel College.