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

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 G...

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Bibliographic Details
Published in:Journal of computational physics 2014-04, Vol.262, p.262-290
Main Authors: Bruno, Oscar P., Delourme, Bérangère
Format: Article
Language:English
Subjects:
Algebra
Analysis of PDEs
Anomalies
Boundary integral methods
Convergence
Diffraction grating
Ewald summation method
Green's functions
Integral equation methods
Lattice sums
Lattices
Mathematics
Numerical Analysis
Quasi-periodic Green function
Rough-surface scattering
Scattering
Scattering by periodic surfaces
Texts
Time-harmonic Helmholtz equation
Time-harmonic Maxwell equations
Two dimensional
Wood anomaly
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Summary: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.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2013.12.047