CV

Education

2021–2025 | PhD (DPhil) in Mathematics (Numerical Analysis), University of Oxford
- Thesis | Structure-preserving FEMs via auxiliary variables: conservative & accurately dissipative integrators/global & local structures for BVPs
- Supervisors | Patrick Farrell, Wayne Arter
2017–2021 | Masters in Mathematics (MMath), University of Oxford
- Grade | First (Distinction)
- Thesis | Computation and approximation properties of near orthogonal matrices for tall random matrices
- Supervisor | Yuji Nakatsukasa

Structure-preserving numerical methods for PDEs & ODEs | Conservative & dissipative integrators / Preserving global & local energy estimates & conservation laws / Asymptotic-preserving integrators / Geometric machine learning
Finite element theory | Finite element exterior calculus (FEEC) / Domain decomposition / Parallel in time (PinT)
Plasma modelling | Magnetohydrodynamics (MHD) / Hybrid fluid-particle models
Turbulent systems | Stabilisation / Preconditioning

Date	Title	Co-authors
16.JUL.2024 (arXiv)	High-order conservative and accurately dissipative numerical integrators via auxiliary variables	Patrick Farrell
Upcoming, Draft available on request	High-order structure-preserving discretisation for ideal MHD arising in the Parker problem	Mingdong He, Kaibo Hu, Patrick Farrell
Upcoming, Draft available on request	High-order conservative–dissipative integrators for reversible–irreversible systems
Upcoming, Draft available on request	An augmented Lagrangian preconditioner for natural convection at high Reynolds number	Alexei Gazca, Benjamin Castellaz, Patrick Farrell
Upcoming, Draft available on request	Globally and locally structure-preserving mixed finite-element methods for boundary-value problems
Upcoming, Draft available on request	High-order fully conservative integrators for integrable ODE systems
Upcoming, Draft available on request	Uniformly accurate magnetic moment–preserving integrators for charged particles
Upcoming	Conservative integrators exhibit greater stability than symplectic integrators on the Toda lattice	Sebastian Ohlig, Patrick Farrell

SEP–OCT.2024 | Supervision of summer intern, Sebastian Ohlig, studying stability of conservative vs. symplectic integrators on the Toda lattice (University of Oxford)
AUG–OCT.2022 | Physics: theory and modelling internship (Tokamak Energy)
JUL–AUG.2019 | Computational fluid dynamics internship (Perm State University)

2024–2025 | Tutor: Computational Mathematics
2023–2024 | Tutor: Prelims corner, Teaching assistant: Numerical Linear Algebra
2021–2022 | Tutor: Analysis I, Teaching assistant: Random Matrix Theory

2021–2025 (DPhil) | EPSRC studentship, UKAEA studentship
2017–2021 (MMath) | Worcester College Foundation scholarship, Worcester College collection prizes

2025 | EMS School on Mathematical Modelling, Numerical Analysis and Scientific Computing* (Kácov, Czechia), Invited talk* (Brown University), Firedrake User Meeting USA* (Fort Worth, Texas), Numerical Mathematics & Scientific Computing seminar* (Rice University)
2024 | Internal seminar* (Rice University), Computing Division technical meeting (UKAEA), Firedrake User Meeting (University of Oxford), PDEsoft (University of Cambridge), European Finite Element Fair (University College London), Exploiting Algebraic and Geometric Structure in Time-integration Methods workshop (University of Pisa), UKAEA PhD student engagement day (UKAEA), Junior Applied Mathematical Seminar (University of Warwick)
2023 | ICIAM 2023 (Waseda University), Numerical analysis group internal seminar (University of Oxford), Junior Applied Mathematics Seminar (University of Oxford), Met Office presentation (University of Oxford), Internal presentation (Tokamak Energy)
2022 | PRISM workshop (Missenden Abbey, UK)

(*scheduled/provisional)