New mathematical and computational techniques for partial differential equations in heterogeneous media

Overview

Mathematical models involving both partial differential equations (PDEs) and heterogeneous media are useful for simulating many important physical processes. This includes:

• groundwater flow
• pollutant transport
• heat transfer
• drug delivery
• tumour growth.

This project focuses on developing new mathematical and computational techniques to solve, simulate and/or analyse PDEs in heterogeneous media.

Research activities

Activities will include:

• developing or applying mathematical techniques
• implementing computational algorithms in MATLAB
• running numerical experiments
• documenting your work in written format.

Outcomes

Potential outcomes from this research include:

• developing new numerical and/or analytical methods for solving PDEs in heterogeneous media
• proposing new coarse-grained models for approximating spatially-averaged solution behaviour of PDEs
• extracting insight into time scales of PDEs, such as the amount of time required to reach a steady state
• developing new methods for parameterising PDEs from experimental data.

Skills and experience

Are you interested in differential equations, computational mathematics and MATLAB programming and wish to broaden your skills and knowledge in these areas? If so, we encourage you to apply.

Any experience in differential equations, computational mathematics and MATLAB is desirable.

Keywords

• applied mathematics
• computational mathematics
• differential equations

Contact

Contact the supervisor for more information, including examples of the types of research problems and past student projects.