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 
Adaptive Numerical Algorithms for the Forward Propagation of Uncertainty in TimeDependent CFD. 

Group  Numerical Analysis and Scientific Computing 
Supervisor  
Description 
Fullyfunded iCASE PhD project supported by IBM Research UK Uncertainty quantification (UQ) is a rapidlyevolving field, incorporating several traditional mathematical disciplines. This project will develop new adaptive numerical algorithms for the forward propagation of uncertainty in largescale timedependent CFD (computational fluid dynamics) simulations and is a collaboration between the School of Mathematics at the University of Manchester and IBM Research UK. The project will be jointly supervised by Dr. Catherine Powell and Professor David Silvester from the School of Mathematics, and Dr. Malgorzata Zimon from IBM Research UK. The PhD student will be based in the School of Mathematics but will also have the opportunity to spend a minimum of 3 months working alongside researchers at IBM Research UK's premises in Daresbury. Project Outline: In realworld applications, when using mathematical models to simulate realworld processes (such as fluid flows) we frequently encounter situations where we are uncertain about one or more of the inputs (viscosity, material parameters, initial conditions, geometry etc). In forward UQ, the main aim is to assess the impact of uncertainty in the model inputs on quantities of interest associated with the model's outputs. For this, we require computationally efficient numerical methods that can take in a probability distribution for the model's inputs and deliver accurate approximations of statistical quantities of interest related to the model's outputs. For timedependent problems, and especially those with nonsmooth solutions, the approximation space often needs to be adapted in time to maintain accuracy. How to design adaptive numerical algorithms with guaranteed error control is highly challenging. Requirements: Candidates with a strong background in applied mathematics and numerical analysis with a passion for solving realworld problems efficiently on computers are encouraged to apply. Some prior experience in scientific computing (Python, MATLAB, C or Fortran etc) is desirable but not essential. Applicants should have (or be on track to to be awarded) either (i) a first class honours MMath degree or (ii) a first class honours BSc degree in Mathematics and a oneyear MSc degree in a relevant mathematical discipline. Ideally, applicants should be available to start in September 2019 or shortly after. How to apply: Informal email queries should be directed to Dr. Catherine Powell and/or Professor David Silvester in the first instance. Formal applications can then be submitted online. As well as transcripts and references, applicants should supply a cover letter describing their academic background and motivation for the project, as well as a complete CV (two pages maximum). These will be considered upon receipt and the PhD position will remain open until it is filled. Funding: For eligible UK applicants, funding covers all tuition fees and annual maintenance payments at the standard EPSRC rate (£15,009 for the academic year 2019/20), plus a CASE topup (amount TBC). For eligible EU applicants, funding is only available to cover tuition fees. 
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 2019 (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. 