PhD Research Project: Adaptive numerical algorithms for PDE problems with random input data

PhD Studentship in Numerical Analysis and Scientific Computing

The project concerns numerical solution of partial differential equations (PDEs) with uncertainty in input data. It will focus on developing adaptive algorithms for efficient solution of such problems. This will involve both rigorous mathematical analysis and extensive numerical experimentation. The algorithms will be designed, analysed, and implemented (in a MATLAB environment).

PDEs are key tools in the mathematical modelling of processes in science and engineering. In practical PDE-based models, precise knowledge of inputs (e.g., material properties, initial conditions, external forces) may not be available, or there might be uncertainty about the inputs. In these cases the models are described by PDEs with random data. Such problems arise in many scientific and industrial contexts when it is essential to accurately model complex processes and perform a reliable risk assessment. One of the major challenges in numerical solution of PDEs with random data is the high dimensionality of the resulting discretisations. Therefore, the development of robust and effective numerical methods which make best use of available computational resources is a very active research area.

The project will provide training in modern numerical analysis and uncertainty quantification techniques, thus equipping the student with highly desirable skills for working in either industry or academia.

 

Entry requirements

We are looking for an enthusiastic and motivated graduate with

• 1st class degree in Mathematics, preferably at the MMath/MSc level, or equivalent;
• A solid background in numerical analysis of PDEs;
• Good programming skills;
• Good communication skills (oral and written).
• Good knowledge of probability theory will be beneficial.

Informal inquiries should be directed to Dr Alex Bespalov, e-mail: a.bespalov@bham.ac.uk

Funding Notes

For UK and EU candidates:

• Funding may be available through a college or EPSRC scholarship in competition with all other PhD applications;
• The scholarship will cover tuition fees, training support, and a stipend at standard rates for 3-3.5 years;
• Early application is strongly recommended;
• The application procedure and deadlines are advertised at https://www.birmingham.ac.uk/schools/mathematics/phd/phd-programme.aspx;
• Strong UK/EU candidates are encouraged to make an informal inquiry.

For non-UK/non-EU candidates:

• Strong self-funded applicants will be considered;
• Exceptionally strong candidates in this category may be awarded a tuition fee waiver (for up to 3 years) in competition with all other PhD applications.