PDEs (partial differential equations) arise in the mathematical modelling of many physical phenomena as well as science and engineering problems (meteorology, structural analysis, fluid dynamics, electromagnetism, finance, etc.) Parallel solution schemes using state-of-the art computers allow scientists to obtain more representative and accurate solutions of the discretised equations faster. This increase in computational and modelling capabilities in turn encourages modelers and scientists to tackle harder problems, which need finer discretisations or more complex geometries. Among these problems, wave propagation in heterogeneous media and time harmonic regime (supposing an oscillatory behaviour in time of the solution) is particularly challenging and requires sophisticated methods. This project seeks to design, analyse, and implement fast, highly-parallel preconditioners for problems involving electromagnetic waves. The PhD researcher will have a substantial interaction with the postdoctoral researchers and scientists working in a recently awarded EPSRC grant between the Universities of Bath and Strathclyde, as well as with the industrial and academic international experts who are collaborating in this project.
Prerequisites: you should have (or expect to have) a UK Honours Degree (or equivalent) in Mathematics, Mathematics and Physics, or a closely related discipline with a high mathematical content. Knowledge of numerical methods for the solution of partial differential equations and programming in usual scientific programming languages is desirable.
The candidates must be a UK citizen, or a EU citizen fulfilling the EPSRC requirements. The starting date of the position should be on the 1st of October, 2018 or very soon after. Funding: 4 year scholarship – EPSRC framework for ‘National Productivity Investment Fund 2018 training Grant’ .
Informal inquiries can be made to the supervisor: V. Dolean
An exciting opportunity is available to students interested in undertaking a Maths PhD with industrial experience. The Numerical Analysis group of the University of Manchester Maths Department, and Sabisu have launched a fully funded EPSRC CASE studentship.
Sabisu is a Manchester based company who produce a software platform for the petrochemicals and chemical production industries. This platform is used for decision support, advanced operational intelligence, data analytics, and managing some of the world’s largest projects. Sabisu uses time series data (among other sources) to identify under-performing assets and predict failures in industrial plants.
The PhD project is concerned with the development of new approaches for clustering of noisy time series, with an application to real-time measurements being taken in large industrial assets. Firstly, the student will investigate low-dimensional representations of time series which preserve relevant features and allow for automatic classification using techniques from machine learning, such as support vector machines. Secondly, the real-time aspect of data collection will necessitate the need for efficient updating techniques in the linear algebra routines underlying the training and assignment phases.
Academic supervisors and industrial partners
The academic supervisors for this project are Dr Martin Lotz and Dr Stefan Güttel. The project is supported by Sabisu, with industrial supervisor Dr Tim Butters and advisor Tim Sharpe. The PhD student will be based at the University of Manchester and work in close collaboration with both the academic and the industrial partners, spending at least three months at Sabisu. A second PhD student will work on a related project in computer science.
The ideal candidate will have a strong interest in Numerical Analysis and Computing. Some experience with at least one of the following mathematical software packages is desired: MATLAB, Python, R, or Julia. Preferably, the applicant is a UK resident, but exceptional candidates from abroad will be consider as well.
How to apply
Please read the information on
and complete your application using the linked Postgraduate Application Page. Please make sure to mention Dr Stefan Güttel and Dr Martin Lotz as your potential supervisors.
The application deadline is Sunday, July 31, 2016.