Implementation of an interior point source in the ultra weak variational formulation through source extraction

Howarth, C. J., Childs, P. N. and Moiola, A. (2014) Implementation of an interior point source in the ultra weak variational formulation through source extraction. Journal of Computational and Applied Mathematics, 271. 295 - 306. ISSN 0377-0427 doi: 10.1016/j.cam.2014.04.017

Abstract/Summary

The Ultra Weak Variational Formulation (UWVF) is a powerful numerical method for the approximation of acoustic, elastic and electromagnetic waves in the time-harmonic regime. The use of Trefftz-type basis functions incorporates the known wave-like behaviour of the solution in the discrete space, allowing large reductions in the required number of degrees of freedom for a given accuracy, when compared to standard finite element methods. However, the UWVF is not well disposed to the accurate approximation of singular sources in the interior of the computational domain. We propose an adjustment to the UWVF for seismic imaging applications, which we call the Source Extraction UWVF. Differing fields are solved for in subdomains around the source, and matched on the inter-domain boundaries. Numerical results are presented for a domain of constant wavenumber and for a domain of varying sound speed in a model used for seismic imaging.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/36618
Identification Number/DOI	10.1016/j.cam.2014.04.017
Refereed	No
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Uncontrolled Keywords	Ultra weak variational formulation; Trefftz method; Helmholtz equation; Time-harmonic acoustic waves; Source extraction; Hankel basis
Publisher	Elsevier
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