A new hybrid integral representation for frequency domain scattering in layered media
Abstract
A variety of problems in acoustic and electromagnetic scattering require the evaluation of impedance or layered media Green's functions. Given a point source located in an unbounded half-space or an infinitely extended layer, Sommerfeld and others showed that Fourier analysis combined with contour integration provides a systematic and broadly effective approach, leading to what is generally referred to as the Sommerfeld integral representation. When either the source or target is at some distance from an infinite boundary, the number of degrees of freedom needed to resolve the scattering response is very modest. When both are near an interface, however, the Sommerfeld integral involves a very large range of integration and its direct application becomes unwieldy. Historically, three schemes have been employed to overcome this difficulty: the method of images, contour deformation, and asymptotic methods of various kinds. None of these methods make use of classical layer potentials in physical space, despite their advantages in terms of adaptive resolution and high-order accuracy. The reason for this is simple: layer potentials are impractical in layered media or half-space geometries since they require the discretization of an infinite boundary. Here in this paper, we propose a hybrid method which combines layer potentials (physical-space)more »
- Publication Date:
- Research Org.:
- New York Univ. (NYU), NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); US Air Force Office of Scientific Research (AFOSR)
- OSTI Identifier:
- 1885636
- Alternate Identifier(s):
- OSTI ID: 1537882; OSTI ID: 1550660
- Grant/Contract Number:
- DEFG0288ER25053; FG02-88ER25053; FA9550-10-1-0180
- Resource Type:
- Published Article
- Journal Name:
- Applied and Computational Harmonic Analysis
- Additional Journal Information:
- Journal Name: Applied and Computational Harmonic Analysis Journal Volume: 45 Journal Issue: 2; Journal ID: ISSN 1063-5203
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; layered media; integral equation; Helmholtz; electromagnetics; Sommerfeld; half-space; scattering
Citation Formats
Lai, Jun, Greengard, Leslie, and O'Neil, Michael. A new hybrid integral representation for frequency domain scattering in layered media. United States: N. p., 2018.
Web. doi:10.1016/j.acha.2016.10.005.
Lai, Jun, Greengard, Leslie, & O'Neil, Michael. A new hybrid integral representation for frequency domain scattering in layered media. United States. https://doi.org/10.1016/j.acha.2016.10.005
Lai, Jun, Greengard, Leslie, and O'Neil, Michael. Sat .
"A new hybrid integral representation for frequency domain scattering in layered media". United States. https://doi.org/10.1016/j.acha.2016.10.005.
@article{osti_1885636,
title = {A new hybrid integral representation for frequency domain scattering in layered media},
author = {Lai, Jun and Greengard, Leslie and O'Neil, Michael},
abstractNote = {A variety of problems in acoustic and electromagnetic scattering require the evaluation of impedance or layered media Green's functions. Given a point source located in an unbounded half-space or an infinitely extended layer, Sommerfeld and others showed that Fourier analysis combined with contour integration provides a systematic and broadly effective approach, leading to what is generally referred to as the Sommerfeld integral representation. When either the source or target is at some distance from an infinite boundary, the number of degrees of freedom needed to resolve the scattering response is very modest. When both are near an interface, however, the Sommerfeld integral involves a very large range of integration and its direct application becomes unwieldy. Historically, three schemes have been employed to overcome this difficulty: the method of images, contour deformation, and asymptotic methods of various kinds. None of these methods make use of classical layer potentials in physical space, despite their advantages in terms of adaptive resolution and high-order accuracy. The reason for this is simple: layer potentials are impractical in layered media or half-space geometries since they require the discretization of an infinite boundary. Here in this paper, we propose a hybrid method which combines layer potentials (physical-space) on a finite portion of the interface together with a Sommerfeld-type (Fourier) correction. We prove that our method is efficient and rapidly convergent for arbitrarily located sources and targets, and show that the scheme is particularly effective when solving scattering problems for objects which are close to the half-space boundary or even embedded across a layered media interface.},
doi = {10.1016/j.acha.2016.10.005},
journal = {Applied and Computational Harmonic Analysis},
number = 2,
volume = 45,
place = {United States},
year = {Sat Sep 01 00:00:00 EDT 2018},
month = {Sat Sep 01 00:00:00 EDT 2018}
}
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https://doi.org/10.1016/j.acha.2016.10.005
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Cited by: 6 works
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