Three-dimensional quasi-periodic shifted Green function throughout the spectrum, including Wood anomalies
Abstract
This work, part II in a series, presents an efficient method for evaluation of wave scattering by doubly periodic diffraction gratings at or near what are commonly called 'Wood anomaly frequencies'. At these frequencies, there is a grazing Rayleigh wave, and the quasi-periodic Green function ceases to exist. We present a modification of the Green function by adding two types of terms to its lattice sum. The first type are transversely shifted Green functions with coefficients that annihilate the growth in the original lattice sum and yield algebraic convergence. The second type are quasi-periodic plane wave solutions of the Helmholtz equation which reinstate certain necessary grazing modes without leading to blow-up at Wood anomalies. Using the new quasi-periodic Green function, we establish, for the first time, that the Dirichlet problem of scattering by a smooth doubly periodic scattering surface at a Wood frequency is uniquely solvable. We also present an efficient high-order numerical method based on this new Green function for scattering by doubly periodic surfaces at and around Wood frequencies. We believe this is the first solver able to handle Wood frequencies for doubly periodic scattering problems in three dimensions. We demonstrate the method by applying it to acoustic scattering.
Additional Information
© 2017 The Author(s) Published by the Royal Society. Received: 5 April 2017. Accepted: 28 September 2017. Data accessibility: All data applicable to this paper are included in the article. Authors' contributions: All authors are equally considered co-contributors in this article. There are no competing interests relevant to this article. This effort was supported by AFOSR, NSF and a NSSEFF Vannevar Bush Fellowship under contracts FA9550-15-1-0043, DMS-1411876 and N00014-16-1-2808 (O.P.B.); NSF DMS-0807325 (S.P.S.); NSF DMS-1312169 and DMS-1614270 (C.T.) and NSF DMS-1211638 (S.V.).Attached Files
Submitted - 1704.01017.pdf
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Additional details
- PMCID
- PMC5719622
- Eprint ID
- 83930
- Resolver ID
- CaltechAUTHORS:20171214-152953856
- FA9550-15-1-0043
- Air Force Office of Scientific Research (AFOSR)
- DMS-1411876
- NSF
- N00014-16-1-2808
- National Security Science and Engineering Faculty Fellowship
- DMS-0807325
- NSF
- DMS-1312169
- NSF
- DMS-1614270
- NSF
- DMS-1211638
- NSF
- Created
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2017-12-15Created from EPrint's datestamp field
- Updated
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2022-03-21Created from EPrint's last_modified field