2,397 research outputs found
Acoustic scattering from locally perturbed periodic surfaces
We prove well-posedness for the time-harmonic acoustic scattering of plane waves from locally perturbed periodic surfaces in two dimensions under homogeneous Dirichlet boundary conditions. This covers sound-soft acoustic as well as perfectly conducting, TE polarized electromagnetic boundary value problems. Our arguments are based on a variational method in a truncated bounded domain coupled with a boundary integral representation. If the quasi-periodic Green's function to the unperturbed periodic scattering problem is calculated efficiently, then the variational approach can be used for a numerical scheme based on coupling finite elements with a boundary element algorithm. Even for a general 2D rough-surface problem, it turns out that the Green's function defined with the radiation condition ASR satisfies the Sommerfeld radiation condition over the half plane. Based on this result, for a local perturbation of a periodic surface, the scattered wave of an incoming plane wave is the sum of the scattered wave for the unperturbed periodic surface plus an additional scattered wave satisfying Sommerfeld's condition on the half plane. Whereas the scattered wave for the unperturbed periodic surface has a far field consisting of a finite number of propagating plane waves, the additional field contributes to the far field by a far-field pattern defined in the half-plane directions similarly to the pattern known for bounded obstacles
Windowed Green Function MoM for Second-Kind Surface Integral Equation Formulations of Layered Media Electromagnetic Scattering Problems
This paper presents a second-kind surface integral equation method for the
numerical solution of frequency-domain electromagnetic scattering problems by
locally perturbed layered media in three spatial dimensions. Unlike standard
approaches, the proposed methodology does not involve the use of layer Green
functions. It instead leverages an indirect M\"uller formulation in terms of
free-space Green functions that entails integration over the entire unbounded
penetrable boundary. The integral equation domain is effectively reduced to a
small-area surface by means of the windowed Green function method, which
exhibits high-order convergence as the size of the truncated surface increases.
The resulting (second-kind) windowed integral equation is then numerically
solved by means of the standard Galerkin method of moments (MoM) using RWG
basis functions. The methodology is validated by comparison with Mie-series and
Sommerfeld-integral exact solutions as well as against a layer Green
function-based MoM. Challenging examples including realistic structures
relevant to the design of plasmonic solar cells and all-dielectric
metasurfaces, demonstrate the applicability, efficiency, and accuracy of the
proposed methodology
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