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Mathematics Institute

Thomas Sales

I am a final year PhD student, supervised by Professor Charles Elliott. My research interests are in numerical/functional analysis, and PDEs. I am currently looking for postdoctoral positions.

About

I completed my MMath at the University of Bath, supervised by Dr Pranav Singh, where my project was about approximate conservation of energy by numerical integrators. In particular, it looked at exponential splitting methods for the time dependent Schrödinger equation. An example of this is the Lie-Trotter splitting

e to the minus i h H u 0 is approximately e to the i h Laplacian e to the minus i h V u 0

A copy of this can be found here, complete with all the typos I submitted it with.

Much of my PhD has been focussed on the Cahn-Hilliard equation (and variants thereof) posed on an evolving surface,

material derivative of u plus tangential divergence of V times u equals laplace beltrami of negative epsilon laplace beltrami of u plus one over epsilon F dash of u

Solution of the Cahn-Hilliard equation with a logartithmic potential on a torus.

Papers/Preprints

  1. C. M. Elliott and T. Sales (2024) - A fully discrete evolving surface finite element method for the Cahn-Hilliard equation with a regular potential (Submitted) (arXiv)
  2. C. M. Elliott and T. Sales (2024) - Navier-Stokes-Cahn-Hilliard equations on evolving surfaces (Accepted) (arXiv)

Teaching:

photo of myself at Oberwolfach

Myself at Mathematisches Forschungsinstitut Oberwolfach.
Photo courtesy of MFO photo collection.

Email: tom.sales 'at' warwick.ac.uk