CV

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Below is an online version of my CV. You can access a PDF version using the link above.

EMPLOYMENT

2025–2027 (predicted) | Postdoctoral Research Associate, Numerical Analysis, University of Oxford
- PROJECT | ERC Starting Grant for Geometric Finite Element Methods (GeoFEM)
- ADVISOR | Kaibo Hu

2021–2025 | PhD (DPhil), Numerical Analysis, University of Oxford
- THESIS | Geometric numerical integration via auxiliary variables
- SUPERVISORS | Patrick Farrell, Wayne Arter
2017–2021 | Integrated Masters (MMath), Mathematics, University of Oxford
- GRADE | First (Distinction)
- THESIS | Computation and approximation of near orthogonal matrices for tall random matrices
- SUPERVISOR | Yuji Nakatsukasa

STRUCTURE-PRESERVING / COMPATIBLE NUMERICAL METHODS FOR PDEs & ODEs | Conservative & dissipative integrators / Global & local energy estimates / Asymptotic-preserving integrators / Geometric ML
FINITE ELEMENT THEORY | FEEC / Domain decomposition / PinT
PLASMA MODELLING | MHD / Hybrid fluid-particle models
TURBULENT SYSTEMS | Stabilisation / Preconditioning

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

Date	Title	Co-authors
29.APR.2025 (arXiv), 31.DEC.2025 (SISC)	Enforcing conservation laws and dissipation inequalities numerically via auxiliary variables	Patrick Farrell

(Upcoming)

Date	Title	Co-authors
20.JAN.2025 (arXiv), 30.APR.2026 (SISC)	Helicity-preserving finite element discretization for magnetic relaxation	Mingdong He, Patrick Farrell, Kaibo Hu

(In review)

Date	Title	Co-authors
28.NOV.2025 (arXiv), In review (CAMWA)	Conservative and dissipative discretisations of multi-conservative ODEs and GENERIC systems	Patrick Farrell

Date	Title	Co-authors
02.NOV.2025 (access)	Geometric numerical integration via auxiliary variables (PhD (DPhil) thesis)

(Drafts available on request)

Title	Co-authors
Automated Galerkin time stepping in Irksome	Pablo Brubeck, Colin Cotter, Patrick Farrell, Rob Kirby, Scott MacLachlan
Enstrophy-stable integrators for the incompressible Navier–Stokes equations	Matin Shams, Patrick Farrell
Energy-stable discretisations of viscoelastic flows	Dennis Trautwein, Patrick Farrell
Energy- and entropy-stable discretisations for the quasi-incompressible Maxwell–Stefan equations	Aaron Brunk, Patrick Farrell, Mária Lukácová-Medviďová
Conservative and accurately dissipative finite element integrators for geometric PDEs	Ganghui Zhang, Patrick Farrell

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

FEB–AUG.2026 | Oscar Benton, MMSC dissertation
- PROJECT | Numerical evolution of magnetic field topologies

FEB–AUG.2025 | Matin Shams, MMSC special projection & dissertation
- PROJECT | Enstrophy-stable integrators for the incompressible Navier–Stokes equations
SEP–OCT.2024 | Sebastian Ohlig, Undergraduate summer internship
- PROJECT | Stability of conservative vs. symplectic integrators on the Toda lattice

2027 | Oberwolfach Workshop on Structure-Preserving Methods* (Oberwolfach Research Institute for Mathematics)
2026 | SciCADE* (University of Edinburgh) / ECCOMAS World Congress on Computational Mechanics* (Munich, Germany) / Invited Seminar (Chinese Academy of Sciences)
2025 | (2×)ACOMEN (Ghent University) / ECCOMAS Thematic Conference on Modern Finite Element Technologies (Aachen, Germany) / Self-Consistency Group Seminar (CHaRMNET) / ACM Colloqium (University of Edinburgh & Heriot-Watt University) / Numerical Mathematics & Scientific Computing Seminar (Rice University) / SIAM CSE (Fort Worth, Texas) / Scientific Computing Seminar (Brown University) / METHODS Group Seminar (Brown University)
2024 | External Seminar (Rice University)

2026 | Firedrake User Meeting* (University of Oxford) / Workshop on Finite Element Tensor Calculus (Tsinghua University)
2025 | Numerical Analysis Group Internal Seminar (University of Oxford) / Biennial Numerical Analysis Conference (University of Strathclyde)
2024 | 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 (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)

JUL.2026 | SciCADE, University of Edinburgh
- TOPIC | Topology-preserving finite element methods for magnetohydrodynamics
- CO-ORGANISERS | Patrick Farrell, Kaibo Hu
- SPEAKERS | Tobias Blickhan, Mingdong He, Gunnar Hornig, Shipeng Mao, Adelle Wright, Anthony Yeates, Qian Zhang
JUN.2025 | Biennial Numerical Analysis Conference, University of Strathclyde
- TOPIC | Structure-preserving finite element methods
- CO-ORGANISERS | Charlie Parker
- SPEAKERS | Aaron Brunk, Mingdong He, Kaibo Hu, Rami Masri

2025–2027 (predicted) | Organisation of the weekly finite element methods reading group, University of Oxford
APR–JUN.2026 | Attendance of the Programme on Differential Complexes at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI), University of Vienna
AUG–OCT.2022 | Physics: theory and modelling internship, Tokamak Energy
JUL.2022 | Plasma physics summer school, UKAEA

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