My research develops fast, mathematically rigorous numerical methods for solving partial differential equations. A common thread is the use of spectral and transform-based ideas to turn hard PDE problems into well-structured linear algebra that can be solved efficiently.
A fast time-frequency hybrid direct solver for the wave equation. Combines a broadband Helmholtz solver with an inverse Fourier transform in frequency space. Includes an interactive simulation tool.
A broadband solver for the Helmholtz equation covering a wide range of frequencies simultaneously, avoiding the need to solve independently at each frequency.
Discretisation of semigroups for IBVPs via the Unified Transform Method (Fokas method), enabling accurate short-time evolution.