|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Efficient Evaluation of Doubly Periodic Green Functions in 3D Scattering, Including Wood Anomaly Frequencies | | Oscar P. Bruno
; Stephen P. Shipman
; Catalin Turc
; Stephanos Venakides
; | | Date: |
4 Jul 2013 | | Abstract: | We present efficient methods for computing wave scattering by diffraction
gratings that exhibit two-dimensional periodicity in three dimensional (3D)
space. Applications include scattering in acoustics, electromagnetics and
elasticity. Our approach uses boundary-integral equations. The quasi-periodic
Green function is a doubly infinite sum of scaled 3D free-space outgoing
Helmholtz Green functions. Their source points are located at the nodes of a
periodicity lattice of the grating.
For efficient numerical computation of the lattice sum, we employ a smooth
truncation. Super-algebraic convergence to the Green function is achieved as
the truncation radius increases, except at frequency-wavenumber pairs at which
a Rayleigh wave is at exactly grazing incidence to the grating. At these "Wood
frequencies", the term in the Fourier series representation of the Green
function that corresponds to the grazing Rayleigh wave acquires an infinite
coefficient and the lattice sum blows up.
At Wood frequencies, we modify the Green function by adding two types of
terms to it. The first type adds weighted spatial shifts of the Green function
to itself with singularities below the grating; this yields algebraic
convergence. The second-type terms are quasi-periodic plane wave solutions of
the Helmholtz equation. They reinstate (with controlled coefficients) the
grazing modes, effectively eliminated by the terms of first type. These modes
are needed in the Green function for guaranteeing the well-posedness of the
boundary-integral equation that yields the scattered field.
We apply this approach to acoustic scattering by a doubly periodic 2D grating
near and at Wood frequencies and scattering by a doubly periodic array of
scatterers away from Wood frequencies. | | Source: | arXiv, 1307.1176 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER