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Time-dependent Scattering Problems

Time dependent wave propagation and scattering is important in acoustics, electromagnetics and seismology.

Number of places

One

Opens

5 March 2018

Eligibility

You will hold (or expect to be awarded) a first or 2:1 UK Honours degree, or overseas equivalent, mathematics or statistics or in a sciences related subject.

Project Details

Time dependent wave propagation and scattering is important in acoustics, electromagnetics and seismology. These problems involve transient wave fields (often short pulses) and give rise to systems of hyperbolic PDEs, which can be approximated directly or first reformulated as boundary integral equations (BIEs) posed on the surface of the scatterer.

The BIE approach is computationally attractive because it only requires quantities to be approximated on a two-dimensional surface, but standard methods are complicated to implement and/or have numerical stability problems which need to be overcome. Recently progress has been made by using time-stepping approximations based on convolution quadrature or other methods which share its "backwards-in-time" framework, but several interesting open problems remain, such as coupling these time-stepping methods to spatial approximations based on B-splines.

The overall aim is to develop reliable and efficient approximation schemes.

Further information

For more information regarding the project please contact Dr Davies´╗┐