Our interests are interdisciplinary, lying at the intersection of applied mathematics, engineering, physics and high-performance computing. Three of our themes are about how we compute: the meshes, the discretisations and the machines. Three are about what we compute with them.
Before any simulation can run, the shape being simulated has to be broken into simpler elements. For high-order methods those elements have to curve to follow the surface, and generating them reliably is one of the largest practical obstacles to using these methods in practice.
Spectral/hp element methods combine the geometric flexibility of finite elements with the accuracy of spectral methods. We work on the discretisations themselves: how to make them stable, how to place resolution where it is needed, and how to couple parts of a simulation that do not line up.
A method is only useful if it runs. We work on making high-order finite element codes fast on the machines that actually exist: many-core CPUs, GPUs, and the exascale systems being built now, where the hardware changes faster than scientific software can usually follow.
Fluids move in two basic ways: smoothly, or chaotically. How they get from one to the other is a century-old question that is still open, and it is the physics underneath most of what else we do, in ordinary fluids and in the plasma inside a fusion reactor alike.
Building a fusion power plant means predicting what happens to a plasma hotter than the centre of the Sun, held in place by magnetic fields, in a machine that does not exist yet. We build the simulation methods and software that this design work will depend on.
Methods are worth having only if they answer questions somebody actually has. We apply high-order simulation to real engineering geometries — racing cars, aircraft wings, fans — usually in cases where the standard industrial approach gives an answer that is not accurate enough to design with.
Our work is supported by the Royal Academy of Engineering, EPSRC, the UK Atomic Energy Authority and industry. Current and recent awards:
Advancing parallel mesh generation and geometry representation to enable industrially relevant, high-fidelity simulations
RAEng Research Chair
Next-generation numerical methods for high-fidelity fusion modelling
NekMesh for industry
NekMesh: towards an industrial high-order mesh generation tool
Cryogenic liquids for net-zero aviation
Modelling cryogenic liquids towards net-zero aviation
NEPTUNE (2022)
NEPTUNE: investigating high-order methods for nuclear fusion
NEPTUNE high-dimensional models
NEPTUNE: high-dimensional models for fusion applications
Exa-UQ
Exa-UQ: uncertainty quantification at the exascale
APinTA
Advanced parallel-in-time algorithms for partial differential equations
NEPTUNE (2020)
NEPTUNE: investigating high-order methods for nuclear fusion
Torin-Sifan KTP
Knowledge Transfer Partnership with Torin-Sifan Ltd
ELEMENT: the exascale mesh network
PRISM: platform for research in simulation methods
ARCHER Leadership Project
ExaFLOW