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Iterative 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

Opens

26 January 2018

Duration

3 years

Eligibility

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

Project Details

Mathematical and numerical modelling is unavoidable nowadays when one tries to investigate and understand complex physical phenomena such as electromagnetic wave propagation. 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). 

There is currently a large international research effort dedicated to the efficient numerical solution frequency-domain or time-harmonic PDEs, driven by the fact that in many applications (including electromagnetic scattering), the frequency-domain formulation is a viable alternative to the time domain, provided suitably-efficient methods are available for solving the large linear systems that arise. Solving wave propagation problems in time-harmonic regime and heterogeneous media is challenging and requires sophisticated methods. This project seeks to design, analyse, and implement fast, highly-parallel DD preconditioners for heterogeneous frequency-domain wave problems involving electromagnetic waves. We will consider coarse grids based on oscillatory basis functions, and introducing another ingredients as absorption will allow us to design methods that are provably efficient, even for general geometries and general decompositions/meshes.

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