High-contrast approximation for penetrable wedge diffractionCitation formats

TY - JOUR

T1 - High-contrast approximation for penetrable wedge diffraction

AU - Nethercote, Matthew

AU - Assier, Raphael

AU - Abrahams, Ian

N1 - Funding Information: Engineering and Physical Sciences Research Council (EPSRC) (DTA studentship to M.A.N., EP/N013719/1 to R.C.A.) and Engineering and Physical Sciences Research Council/United Kingdom Research and Innovation (EPSRC/UKRI) (EP/K032208/1 and EP/R014604/1 to I.D.A.). Publisher Copyright: © 2019 The Author(s) 2020. Published by Oxford University Press. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/4/30

Y1 - 2020/4/30

N2 - 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 infinitely many solutions to (possibly inhomogeneous) impenetrable wedge problems. Each impenetrable problem is solved using a combination of the Sommerfeld-Malyuzhinets and Wiener-Hopf techniques. The resulting approximated 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.

AB - 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 infinitely many solutions to (possibly inhomogeneous) impenetrable wedge problems. Each impenetrable problem is solved using a combination of the Sommerfeld-Malyuzhinets and Wiener-Hopf techniques. The resulting approximated 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.

KW - penetrable wedge

KW - wave diffraction

U2 - https://doi.org/10.1093/imamat/hxaa011

DO - https://doi.org/10.1093/imamat/hxaa011

M3 - Article

VL - 85

SP - 421

EP - 466

JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

SN - 0272-4960

IS - 3

ER -