Rapidly convergent two-dimensional quasi-periodic Green function throughout the spectrum-including Wood anomalies

Authors:
Oscar P. Bruno;Bérangère Delourme
Affiliations:
Computing and Mathematical Sciences, Caltech, Pasadena, CA 91125, USA;Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), 99 Av. J-B Clément, F-93430 Villetaneuse, France
Venue:
Journal of Computational Physics
Year:
2014

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Abstract

We introduce a new methodology, based on new quasi-periodic Green functions which converge rapidly even at and around Wood-anomaly configurations, for the numerical solution of problems of scattering by periodic rough surfaces in two-dimensional space. As is well known the classical quasi-periodic Green function ceases to exist at Wood anomalies. The approach introduced in this text produces fast Green function convergence throughout the spectrum on the basis of a certain ''finite-differencing'' approach and smooth windowing of the classical Green function lattice sum. The resulting Green-function convergence is super-algebraically fast away from Wood anomalies, and it reduces to an arbitrarily-high (user-prescribed) algebraic order of convergence at Wood anomalies.