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Boris Andrews
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
[1] Boris D. Andrews, Patrick E. Farrell: High-order conservative and accurately dissipative numerical integrators via auxiliary variables. arXiv (2024). https://doi.org/10.48550/arXiv.2407.11904
[...] we propose an approach for the construction of timestepping schemes that preserve dissipation laws and conserve multiple general invariants, via finite elements in time and the systematic introduction of auxiliary variables. [...] We [devise] novel arbitrary-order schemes that conserve to machine precision all known invariants of Hamiltonian ODEs [...] and arbitrary-order schemes for the compressible Navier–Stokes equations that conserve mass, momentum, and energy, and provably possess non-decreasing entropy.
[2] P. Alexei Gazca-Orozco, Boris D. Andrews: An augmented Lagrangian preconditioner for natural convection at high Reynolds number. Upcoming
Year | Subject | Role |
2024–2025 | Computational Mathematics | Tutor |
2023–2024 | "Prelims Corner" | Tutor |
C6.1 Numerical Linear Algebra | TA (Marker) | |
2021–2022 | C7.7 Random Matrix Theory | TA |
M2 Analysis I | Tutor |
Hi! I'm Boris Andrews, and I'm a 3rd-year (of 4) DPhil (PhD) candidate in the numerical analysis research group, here at the University of Oxford, working on structure-preserving numerical methods for PDEs.
Thesis: High-order conservative and accurately dissipative numerical integrators via auxiliary variables
Supervisors: Patrick Farrell | Wayne Arter
Short CV:
- 2021–2025*: Doctor of Philosophy (DPhil/PhD), Mathematical Institute, University of Oxford
- 2017–2021: Master of Mathematics (MMath), Worcester College, University of Oxford
*predicted
2021–present (DPhil):
- EPSRC studentship: £~70,000
- UKAEA studentship: £~12,000
2017–2021 (MMath):
- Worcester College Foundation scholarship: £~200
- Worcester College collection prizes: £~160
Numerical methods for PDEs/ODEs:
Structure-preserving methods:
- Conservative integrators
- Symplectic integrators
- Local/global energy estimates
Finite element theory:
- Finite elements in time (FET)
- High-order methods
- Finite element exterior calculus (FEEC)
- Parallelization in time (PinT)
Hybrid fluid-particle models
Turbulent systems:
- Stabilisation
- Robust preconditioning (incl. multigrid)
Mathematical modelling:
Fluid models:
- Navier–Stokes equation (incl. compressible)
- Magnetohydrodynamics (MHD)
Gyrokinetic theory/drift mechanics
Plasma (incl. fusion plasmas)
Hybrid fluid-kinetic models