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Numerical Computation of Resonances and Pseudospectra in Acoustic Scattering

Lanzoni, J; (2016) Numerical Computation of Resonances and Pseudospectra in Acoustic Scattering. Doctoral thesis , UCL (University College London). Green open access

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Abstract

Acoustic scattering is a well-known physical phenomenon which arises in a wide range of fields: when acoustic waves propagating in a medium impinge on a localised non-uniformity, such as a density fluctuation or an external obstacle, their trajectories are deviated and scattered waves are generated. A key role in scattering theory is played by resonances; these are particular scatterer-dependent non-physical ‘complex’ frequencies at which acoustic scattering exhibits exceptional behaviour. The study of acoustic resonances for a particular scatterer provides an insight in the behaviour that the acoustic scattering assumes at the near physical ‘real’ frequencies, and it is a fundamental step in many applications. Yet, the numerical computation of resonances and pseudospectra - a mathematical tool which can be used to study the influence of resonances on physical frequencies - remains very expensive. With the present Thesis we want to address this particular problem, by proposing numerical algorithms based on the Boundary Element Method (BEM) for computing resonances and pseudospectra and by analysing their efficiency and performance. Finally, we apply such algorithms to half a dozen of physically relevant scatterer, inspired from different fields where acoustic scattering plays a relevant role.

Type: Thesis (Doctoral)
Title: Numerical Computation of Resonances and Pseudospectra in Acoustic Scattering
Event: UCL
Open access status: An open access version is available from UCL Discovery
Language: English
Keywords: resonances, pseudospectra, numerical algorithms, acoustic scattering
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI: http://discovery.ucl.ac.uk/id/eprint/1474317
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