DrSteven Dargaville

My research has two main strands: the development of mathematical models for energy systems and numerical methods for asymmetric linear systems. I am particularly interested in multi-physics problems involving heavy coupling and the design of algorithms that enable accurate and scalable computation on modern high-performance computers.

My doctoral research examined modelling of LiFePO₄ batteries, a chemistry that exhibits a phase transition during charge and discharge. This work involved solving large, coupled systems of nonlinear partial differential equations using finite-volume discretisation, parallel Newton–Krylov methods, and extensive comparison with experimental data.

Subsequently my research has centred on computational methods for Boltzmann transport problems, including applications in civil nuclear systems (fission and fusion), coupled fluid dynamics/radiative transfer, lattice Boltzmann for fluids and spectral-wave modelling. My work in this area explores adaptive discretisation strategies, finite element and wavelet-based formulations across space–angle–energy phase-space, and scalable solvers for high performance computers (both CPUs and GPUs). This has been supported by industrial and government partners, in the UK and internationally.

I also contributed to the RAMP, PROTECT, TRACK and TRACK2 projects focused on modelling the risk of COVID-19 infection in indoor spaces. This involved extensive collaboration with researchers and scientists from the Universities of Leeds, Cambridge, Newcastle and Manchester, the UK Health and Safety Authority (UKHSA), Defence Science and Technology Laboratory and the Department for Transport (DfT). My work used computational fluid dynamics to simulate indoor airflow and compare predictions with experimental data, supporting policy recommendations subsequently adopted across the UK.

I have developed two main pieces of scientific software over the past decade. I am the lead developer of FETCH2 (link), a multi-physics code used for radiation transport research at Imperial College London and in partnership with organisations across academia and industry. I also created PFLARE (link), an open-source solver for asymmetric linear systems that is now available in the PETSc configure. The methods I developed in PFLARE have demonstrated scalability across pre-exascale GPU machines in advection-dominated problems without Gauss-Seidel iterations, addressing a long-standing open problem in the field.

I have extensive teaching and supervisory experience across undergraduate, MSc and PhD levels in both mathematics and engineering programmes. At Imperial, I most recently co-wrote and lectured the Advanced Programming module within the MSc in Applied Computational Science and Engineering, aimed at equipping students with practical high-performance computing skills. I have supervised and mentored undergraduate, MSc and PhD students across a range of topics, including fluid dynamics, radiation transport and AI methods.