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Preconditioners for time-harmonic heterogeneous electromagnetic problems

The underlying mathematical model in this case is Maxwell’s equations - according to applications it can take two different forms (time-domain and time-harmonic).

Number of places

1

Funding

Home fee, Stipend

Opens

26 January 2018

Duration

4 years

Eligibility

You should have (or expect to have) a UK Honours Degree (or equivalent) at 2.1 or above in Mathematics

Project Details

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

Suggested reading (on possible applications of Maxwells equations and the need for efficient solvers):   https://sinews.siam.org/Details-Page/high-performance-computing-for-the-detection-of-strokes-2

Funding Details

4 year scholarship - EPSRC framework for ‘National Productivity Investment Fund 2018 training Grant’