Math @ Duke

Publications [#330399] of Stephanos Venakides
Papers Published
 Bruno, OP; Shipman, SP; Turc, C; Stephanos, V, Threedimensional quasiperiodic shifted Green function throughout the spectrum, including Wood anomalies.,
Proceedings. Mathematical, Physical, and Engineering Sciences, vol. 473 no. 2207
(November, 2017),
pp. 20170242, The Royal Society [doi]
(last updated on 2019/07/23)
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 quasiperiodic 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 quasiperiodic plane wave solutions of the Helmholtz equation which reinstate certain necessary grazing modes without leading to blowup at Wood anomalies. Using the new quasiperiodic 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 highorder 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.


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