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SUMMARY:High-contrast approximation for penetrable wedge diffraction - Mat
 thew Nethercote (University of Manchester)
DTSTART:20190823T140000Z
DTEND:20190823T143000Z
UID:TALK128983@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION: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 materia
 l property of the host and the wedge scatterer\, is assumed small. The rel
 evant material property depends on the physical context and is different f
 or acoustic and electromagnetic waves for example. Based on this assumptio
 n\, 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 s
 olved using a combination of the Sommerfeld-Malyuzhinets and Wiener-Hopf t
 echniques. The resulting approximate solution to the penetrable wedge invo
 lves a large number of nested complex integrals and is hence difficult to 
 evaluate numerically. In order to address this issue\, a subtle method (co
 mbining 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 lea
 ds to a clear improvement on extant approaches.
LOCATION:Seminar Room 2\, Newton Institute
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