TY - JOUR
T1 - Three-dimensional quasi-periodic shifted Green function throughout the spectrum, including Wood anomalies
AU - Bruno, Oscar P.
AU - Shipman, Stephen P.
AU - Turc, Catalin
AU - Venakides, Stephanos
N1 - Publisher Copyright:
© 2017 The Author(s) Published by the Royal Society. All rights reserved.
PY - 2017/11/1
Y1 - 2017/11/1
N2 - 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 blowup 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.
AB - 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 blowup 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.
KW - Boundary-integral equations
KW - Electromagnetic computation
KW - Lattice sum
KW - Periodic Green function
KW - Scattering
KW - Wood anomaly
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U2 - 10.1098/rspa.2017.0242
DO - 10.1098/rspa.2017.0242
M3 - Article
AN - SCOPUS:85037737384
SN - 1364-5021
VL - 473
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2207
M1 - 20170242
ER -