Since September 2020, I have been studying for a PhD in the School of Mathematical Sciences at the University of Nottingham.

My project title is currently ‘Finite Element Methods for Fluid-Structure Interaction Problems‘ and is supervised by Paul Houston, Matthew Hubbard, and Reuben O’Dea.

As part of my preliminary learning, I have created a 1D discontinuous Galerkin FEM solver which uses error indicators to adaptively h- and p-refine. You can find it on GitHub, or you can give a very basic online version a go.

I also do a small amount of teaching. I recently taught/demonstrated for first year Mathematics and Natural Sciences students in programming with Python.

Reports

PhD First Year Report

  • Broad overview of FEM and placenta literature
  • Introduction to hp-FEM
  • DGFEM discretisations of Poisson’s equation and Stokes flow
  • 1D residual error indicators
  • Design of an OOP FEM code

PhD Second Year Report

  • Broad overview of FEM and placenta literature
  • Blood flow modelling as porous medium
  • Simple blood flow simulations in representative 2D geometries
  • Synthetic MRI generation, toward model validation
  • Model development: septal veins, nutrient transport, and variable permeabilit

Academic Talks

A Recipe for Adaptive hp-FEMs (April 2021)

  • Overview of FEMs
  • Interactive example
  • C++ implementation & numerical experiments
  • hp-adaptive FEMs in action
  • Possible extensions

Placental Haemodynamics (December 2021)

  • Introduction to FEMs and placentas
  • Modelling of porous media
  • “box-circle” Darcy-Brinkman flow results
  • Outlook

Placental Haemodynamics (May 2022)

  • Modified version of December 2021 talk
  • Introduction to FEMs and placentas
  • Modelling of porous media
  • “box-circle” Darcy-Brinkman flow results
  • “inverted-circle-slice-6” Darcy-Brinkman flow results
  • Outlook

Placental Haemodynamics (September 2022)

  • Modified version of May 2022 talk
  • Introduction to FEMs, placentas, and porous medium modelling
  • Placentone and 2D placenta slice flow results
  • Flow comparison with septal veins
  • Oxygen transport
  • Immediate next steps

Placental Haemodynamics (November 2022)

  • Modified version of September 2022 talk
  • Introduction to FEMs, placentas, and porous medium modelling
  • Placentone and 2D placenta slice flow results
  • Flow comparison with septal veins
  • Oxygen transport
  • Immediate next steps

Outreach Talks

Maths “Careers” Talk (February 2021)

  • Background
  • Experiences
  • Work experiences
  • Day-to-day on the PhD
  • PhD top tips

Teaching

Core and MTHS1001 Python (2020–2022)

  • First year programming
  • Introduction to variables and data structures
  • Basic plotting

MATH4063 Scientific Computation and C++ (2022)

  • Fourth year programming
  • Basic control and data structures
  • Memory management
  • Object-oriented programming