Windowed Green function method for the Helmholtz equation in the presence of multiply layered media
- Creators
- Bruno, O. P.
- Pérez-Arancibia, C.
Abstract
This paper presents a new methodology for the solution of problems of two- and three-dimensional acoustic scattering (and, in particular, two-dimensional electromagnetic scattering) by obstacles and defects in the presence of an arbitrary number of penetrable layers. Relying on the use of certain slow-rise windowing functions, the proposed windowed Green function approach efficiently evaluates oscillatory integrals over unbounded domains, with high accuracy, without recourse to the highly expensive Sommerfeld integrals that have typically been used to account for the effect of underlying planar multilayer structures. The proposed methodology, whose theoretical basis was presented in the recent contribution (Bruno et al. 2016 SIAM J. Appl. Math. 76, 1871–1898. (doi:10.1137/15M1033782)), is fast, accurate, flexible and easy to implement. Our numerical experiments demonstrate that the numerical errors resulting from the proposed approach decrease faster than any negative power of the window size. In a number of examples considered in this paper, the proposed method is up to thousands of times faster, for a given accuracy, than corresponding methods based on the use of Sommerfeld integrals.
Additional Information
© 2017 The Author(s). Published by the Royal Society. Received: 2 March 2017; Accepted: 11 May 2017; Published 14 June 2017. This work was supported by NSF and AFOSR through contracts DMS-1411876 and FA9550-15-1-0043, and by the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808. Authors' contributions: O.P.B. and C.P.-A. contributed to all aspects of this article. We declare we have no competing interests.Attached Files
Submitted - 1703.01034.pdf
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Additional details
- PMCID
- PMC5493953
- Eprint ID
- 79120
- Resolver ID
- CaltechAUTHORS:20170717-085623869
- DMS-1411876
- NSF
- FA9550-15-1-0043
- Air Force Office of Scientific Research (AFOSR)
- N00014-16-1-2808
- National Security Science and Engineering Faculty Fellowship
- Vannever Bush Faculty Fellowship
- Created
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2017-07-17Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field