Novel techniques for modelling with partial differential equations in heterogeneous media

Study level


Master of Philosophy


Vacation research experience scheme

Topic status

We're looking for students to study this topic.


Dr Elliot Carr
Senior Lecturer
Division / Faculty
Science and Engineering Faculty


Mathematical models involving heterogenous media comprising two or more constituent materials with different physical properties are widespread across scientific and engineering disciplines.

For example, modelling the flow of pollutants or water below the earth’s surface involves dealing with a highly heterogeneous geological structure.

Solving such mathematical models is particularly challenging when the heterogeneity is explicitly accounted for in the model.

As a result this project aims to answer natural questions such as:

  • Can we develop accurate and efficient numerical or semi-analytical methods to solve such models?
  • Can we develop simple efficient models that smooth out the heterogeneity but remain accurate?
  • Can we develop mathematical techniques for extracting insight into the process without solving the original model?

Research activities

You will meet regularly with Dr Carr to acquire new knowledge, brainstorm ideas, discuss your progress and receive feedback and direction on your work.

This project will involve pen and paper derivations and calculations, developing code in MATLAB and communicating your work in written form.


You will develop new skills in:

  • partial differential equations
  • computational mathematics
  • programming (MATLAB)
  • mathematical writing
  • LaTeX typesetting.

New techniques/knowledge/results generated during your project will be published in leading mathematical/scientific journals.

Skills and experience

This project can be tailored to your study level whether you are an undergraduate (VRES), Honours, Masters or PhD student. This topic can also be personalised to suit your individual interests and skills.

Ideally, the successful student will have some prior experience with solving ordinary or partial differential equations in MATLAB.


You may be able to apply for a research scholarship in our annual scholarship round.

Annual scholarship round



Please contact Dr Carr via email to express your interest in this project.