The Ultra Weak Variational Formulation (UWVF) is a powerful numerical method for the simulation of acoustic, elastic, and electromagnetic waves. Key to its strength is the superior approximation properties of the Trefftz basis of local solutions of the homogeneous form of the equation to be solved. In this thesis we consider time harmonic acoustic wave propagation in two dimensions, as modelled by the Helmholtz equation. We investigate enrichment of the UWVF basis for wave scattering and propagation problems, with applications in geophysics. A new Hankel basis is implemented in the UWVF, allowing greater flexibility than the traditional plane wave basis. We use ray tracing techniques to provide a good a priori choice of direction of propagation for the UWVF basis. A reduction in the number of degrees of freedom required for a given level of accuracy is achieved for the case of scattering by a smooth convex obstacle. The use of the UWVF for forward seismic modelling is considered, simulating wave propagation through a synthetic sound speed profile of the subsurface of the Earth. The practicalities of implementation in a domain of highly varying sound speed are discussed, and a ray enhanced basis is trialled. Wave propagation from a source on the interior of the domain is simulated, representative of an explosive sound source positioned at depth. The UWVF typically has difficulties representing the inhomogenous Helmholtz equation. An augmentation to the UWVF called the Source Extraction UWVF is presented which allows the superior approximation properties of the Trefftz basis to be maintained.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:631703 |
| Date | January 2014 |
| Creators | Howarth, Charlotta Jasmine |
| Publisher | University of Reading |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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