High-contrast approximation for penetrable wedge diffraction

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• Matthew Nethercote (University of Manchester)
• Friday 23 August 2019, 15:00-15:30
• Seminar Room 2, Newton Institute.

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WHT - Bringing pure and applied analysis together via the Wiener-Hopf technique, its generalisations and applications

The important open canonical problem of wave diffraction by a penetrable wedge is considered in the high-contrast limit. Mathematically, this means that the contrast parameter, the ratio of a specific material property of the host and the wedge scatterer, is assumed small. The relevant material property depends on the physical context and is different for acoustic and electromagnetic waves for example. Based on this assumption, a new asymptotic iterative scheme is constructed. The solution to the penetrable wedge is written in terms of an infinite sequence of (possibly inhomogeneous) impenetrable wedge problems. Each impenetrable problem is solved using a combination of the Sommerfeld-Malyuzhinets and Wiener-Hopf techniques. The resulting approximate solution to the penetrable wedge involves a large number of nested complex integrals and is hence difficult to evaluate numerically. In order to address this issue, a subtle method (combining asymptotics, interpolation and complex analysis) is developed and implemented, leading to a fast and efficient numerical evaluation. This asymptotic scheme is shown to have excellent convergent properties and leads to a clear improvement on extant approaches.

This talk is part of the Isaac Newton Institute Seminar Series series.

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