Many problems in applied mathematics require the reconstruction or extrapolation of a surface based on (limited) measured data points on the surface.
An example of this includes reconstructing physical surfaces from information in photographic, point scanner or medical imaging data. Less obvious examples include extending a mathematical surface defined only locally to something defined globally: this has application in modelling moving interfaces in fluids.
With these problems it's important to consider how to accurately and efficiently calculate the surface and how to ensure it meets the required properties.
This project would involve one or more complementary approaches in designing computational algorithms for surface fitting and extrapolation, based on your background and interests.
We expect to uncover new insights and understandings related to the research project. We also intend to develop software as well as publish a series of research articles.
Skills and experience
In order to be considered for this project, you should have skills and/or experience in computational methods in MATLAB.
It would also be desirable if you have skills and/or experience in partial differential equations, computational linear algebra and high performance computing.
You may be able to apply for a research scholarship in our annual scholarship round.
Contact the supervisor for more information.