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Convolution quadrature methods for transient and broadband wave modelling S&T21

  • School: School of Science and Technology
  • Study mode(s): Full-time / Part-time
  • Starting: 2022
  • Funding: UK student / EU student (non-UK) / International student (non-EU) / Fully-funded


NTU's Fully-funded PhD Studentship Scheme 2022

Project ID: S&T21

The understanding and prediction of wave behaviour is important for a wide range of applications in acoustics, elasticity, electromagnetics and quantum mechanics. Fully time-dependent wave models are essential when the wave sources themselves undergo fundamental changes. Examples include acoustic emissions in the presence of structural fatigue (such as in the condition monitoring of bridges, for example) and vibrations induced by a structural shock (such as in vehicle crash testing). Time-dependent models are also needed in acoustics for virtual design and auralisation, the process of simulating how a room or space would sound in real time that is used to improve the acoustics in buildings. The broadband frequency content typically present in such models makes them highly challenging for mathematical modelling via numerical simulation methods, due to large computational overheads. This research aims to develop novel hybrid methodologies for time-dependent waves by combining numerical wave simulation methods that are most efficient at low frequencies and asymptotic models for high frequencies. The coupling of these approaches will take place within the framework of the so-called Convolution Quadrature (CQ) method.

Recent work has highlighted that since the CQ becomes increasingly dissipative for higher frequency wave content, then accurate modelling of early wave reflections is of particular importance here. We therefore propose to adopt the mirror image-source method to provide an efficient approach for high frequencies to speed up the CQ based scheme and permit the solution of large-scale three-dimensional problems of interest to our industrial collaborators (recent collaborators include PACSYS Ltd., Jaguar Land Rover Ltd., Far UK Ltd., InuTech GmbH and CDH AG). Furthermore, at low frequencies the method of fundamental solutions (MFS) appears to provide the ideal partner to the image source method, since it is also based on expanding the solution in terms of Green’s functions with both a simpler implementation process and often faster convergence than many common alternatives, such as finite or boundary elements.  The MFS does, however, require a choice for the locations of a set of source points for the corresponding Green’s functions that we plan to optimise using modern physics-informed deep learning based techniques.

The main goal of the project is to develop enhanced (in terms of speed and accuracy) simulation algorithms for virtual design with applications across acoustics and mechanical engineering. The development of enhanced simulation methods saves energy, costs and resource usage by manufacturers through the reduction in physical prototyping via virtual prototypes and digital twins.

The project would ideally suit a highly motivated candidate with a passion for the mathematical modelling of problems arising in industry. A good background in partial differential equations, a willingness to develop your skills in scientific computing would also be beneficial.

The supervisory team consists of Director of Studies Dr David Chappell and co supervisors Dr Archontis Giannakidis and Dr Martin Richter (University of Nottingham).

School strategic research priority

The project aligns with the IMEC research centre and especially the growth research area of Sustainable Engineering.

Entry qualifications

For the eligibility criteria, visit our studentship application page.

How to apply

For guidance and to make an application, please visit our studentship application page. The application deadline is Friday 14 January 2022.

Fees and funding

This is part of NTU's 2022 fully-funded PhD Studentship Scheme.

Guidance and support

Download our full applicant guidance notes for more information.

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