@inbook{5aba8602945a470184c9dcae3827aeab,
title = "Changes in the far-field pattern induced by rounding the corners of a scatterer: dependence upon curvature",
abstract = "In this chapter, we rigorously examine the differences in the far-field patterns (9.1) for an E-polarised scatterer with a single corner. The scattering of a plane wave by such a scatterer is formulated in Section 9.1, and an appropriate integral equation for the surface distribution on the obstacle is given. As a motivation for the analysis to follow, a brief discussion of numerical results is given in Section 9.2. In Section 9.3, the lemniscate (having a right-angled corner) and its rounded counter-part is used as a test case to establish analytic bounds for the maximum difference in the far field. An integral equation is obtained for the difference in the surface distributions on each obstacle; its approximate solution is shown to be O((kp) 2/3), as kp -> 0 (Theorem 9.1). It then follows that the non-dimensionalised far-field difference √κ∥μο-μρ∥∞ is O((kp) 4/3), as kp -> 0 (Theorem 9.2). ",
keywords = "Analytic bounds, E-polarised scatterer, Electromagnetic wave scattering, Far-field patterns, Integral equation, Integral equations, Plane wave scattering, Surface distribution",
author = "Markowskei, {Audrey J.} and Smith, {Paul D.}",
year = "2020",
doi = "10.1049/SBEW528E_ch9",
language = "English",
isbn = "9781785613845",
series = "The ACES Series on Computational and Numerical Modelling in Electrical Engineering",
publisher = "Institution of Engineering and Technology",
pages = "215--240",
editor = "Kazuya Kobayashi and Smith, {Paul Denis}",
booktitle = "Advances in mathematical methods for electromagnetics",
address = "United Kingdom",
}