Numerical Analysis and Scientific Computing PhD projects
This page provides a (partial) list of specific (and not so specific) PhD projects currently offered around the Numerical Analysis and Scientific Computing topic.
Identifying an interesting, worthwhile and doable PhD project is not a trivial task since it depends crucially on the interests and abilities of the student (and the supervisor!) The list below therefore contains a mixture of very specific projects and fairly general descriptions of research interests across the School. In either case you should feel free to contact the potential supervisors to find out more if you're interested.
You should also explore the School's research groups' pages, and have a look around the homepages of individual members of staff to find out more about their research interests. You may also contact us for general enquiries.
Title 
Fast and Reliable Algorithms for High Peformance Numerical Linear Algebra 

Group  Numerical Analysis and Scientific Computing 
Supervisor  
Description 
The project focuses on developing a new generation of numerical linear algebra algorithms that exploit current and future computers. The algorithms need to be fast and to be accompanied by rigorous error analysis to guarantee their reliability, even for the largest and most difficult problems. The target problems will be drawn from linear equations, linear least squares problems, eigenvalue problems, the singular value decomposition, and matrix function evaluation. These are the innermost kernels in many scientific and engineering applicationsin particular, in data science and in machine learningso it is essential that they are fast, accurate, and reliable. Funding NotesOpen to all. Funding is available and would provide fees and maintenance at RCUK level for home/EU students, or a feesonly bursary for overseas students. 
Title 
Fluidstructure interaction effects in the sedimentation of thin elastic sheets 

Group  Numerical Analysis and Scientific Computing 
Supervisors 

Description 
There is much current interest in socalled twodimensional materials The aim of this project is to perform a systematic study of  the effect of the sheets' aspect ratio; long narrow sheets are  the effect of wrinkling instabilities and the development of The focus of this specific project is on computational/semianalytical
COSUPERVISORS: Professor Anne Juel (School of Physics and Astronomy) START DATE: September 2018 (or as soon as possible thereafter) OTHER ASSOCIATED PROJECT AREAS: Physics FUNDING: Funding is available and would provide fees and maintenance DEADLINE: Applications are accepted at any time until the position 
Title 
Scheduling and Parallel Computing 

Group  Numerical Analysis and Scientific Computing 
Supervisor  
Description 
Consider a large computational task, for instance, solving a large system of linear equations. This task can be split into many smaller jobs which are then scheduled and queued at a large number of different heterogeneous computing resources and are executed in parallel. The processing requirements of the different resources (for instance CPUs and GPUs) are different, and they may well have different communication costs. In this project we will be interested in understanding the stochastic effects before designing (and implementing) novel distributed scheduling algorithms. 
Title 
Numerical Analysis and Computational Methods for Solving PDEs with Uncertainty 

Group  Numerical Analysis and Scientific Computing 
Supervisor  
Description 
Uncertainty Quantification (UQ) is the science of accounting for uncertainty in mathematical models. Research in this area has undergone rapid growth in the last few years and is currently considered a 'hot topic'. This growth has been driven by the need for scientists in today's world to provide decision makers with ever more accurate and reliable predictions that are based on results obtained from mathematical models. Many physical processes such as fluid flows are governed by partial differential equations (PDEs). In practical applications in the real world, it is unlikely that all the inputs (boundary conditions, geometry, coefficients) for the chosen PDE model will be known. One possibility is to model the quantities that we don't know as random variables. Solving these problems is not always hard in theory but solving them efficiently in practice is a massive challenge. I am interested in working with students who want to develop numerical analysis and numerical methods for solving partial differential equations with uncertain inputs. I welcome any enquiries to work in this area. Specific projects could be theoretical or computational, according to the strengths of the student. Projects on this topic would suit students who have taken undergraduate courses in numerical analysis and applied mathematics who have a keen interest in computational mathematics and developing practical algorithms. Some prior programming experience is essential. Background reference: An Introduction to Computational Stochastic PDEs (Cambridge Texts in Applied Mathematics), G. J. Lord, C.E. Powell and T. Shardlow, 2014. 
Title 
Integral Geometry of Cones 

Group  Numerical Analysis and Scientific Computing 
Supervisor  
Description 
Science and technology depends increasingly on the efficient acquisition, storage and processing of vast amounts of data. 