887 research outputs found
Windowed Green Function method for layered-media scattering
This paper introduces a new Windowed Green Function (WGF) method for the
numerical integral-equation solution of problems of electromagnetic scattering
by obstacles in presence of dielectric or conducting half-planes. The WGF
method, which is based on use of smooth windowing functions and integral
kernels that can be expressed directly in terms of the free-space Green
function, does not require evaluation of expensive Sommerfeld integrals. The
proposed approach is fast, accurate, flexible and easy to implement. In
particular, straightforward modifications of existing (accelerated or
unaccelerated) solvers suffice to incorporate the WGF capability. The
mathematical basis of the method is simple: the method relies on a certain
integral equation posed on the union of the boundary of the obstacle and a
small flat section of the interface between the penetrable media. Numerical
experiments demonstrate that both the near- and far-field errors resulting from
the proposed approach decrease faster than any negative power of the window
size. In the examples considered in this paper the proposed method is up to
thousands of times faster, for a given accuracy, than a corresponding method
based on the layer-Green-function.Comment: 17 page
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
Windowed Green Function Method for Nonuniform Open-Waveguide Problems
This contribution presents a novel Windowed Green Function (WGF) method for
the solution of problems of wave propagation, scattering and radiation for
structures which include open (dielectric) waveguides, waveguide junctions, as
well as launching and/or termination sites and other nonuniformities. Based on
use of a "slow-rise" smooth-windowing technique in conjunction with free-space
Green functions and associated integral representations, the proposed approach
produces numerical solutions with errors that decrease faster than any negative
power of the window size. The proposed methodology bypasses some of the most
significant challenges associated with waveguide simulation. In particular the
WGF approach handles spatially-infinite dielectric waveguide structures without
recourse to absorbing boundary conditions, it facilitates proper treatment of
complex geometries, and it seamlessly incorporates the open-waveguide character
and associated radiation conditions inherent in the problem under
consideration. The overall WGF approach is demonstrated in this paper by means
of a variety of numerical results for two-dimensional open-waveguide
termination, launching and junction problems.Comment: 16 Page
Windowed Integral Equation Methods for Problems of Scattering by Defects and Obstacles in Layered Media
This thesis concerns development of efficient high-order boundary integral equation methods for the numerical solution of problems of acoustic and electromagnetic scattering in the presence of planar layered media in two and three spatial dimensions. The interest in such problems arises from application areas that benefit from accurate numerical modeling of the layered media scattering phenomena, such as electronics, near-field optics, plasmonics and photonics as well as communications, radar and remote sensing.
A number of efficient algorithms applicable to various problems in these areas are pre- sented in this thesis, including (i) A Sommerfeld integral based high-order integral equation method for problems of scattering by defects in presence of infinite ground and other layered media, (ii) Studies of resonances and near resonances and their impact on the absorptive properties of rough surfaces, and (iii) A novel Window Green Function Method (WGF) for problems of scattering by obstacles and defects in the presence of layered media. The WGF approach makes it possible to completely avoid use of expensive Sommerfeld integrals that are typically utilized in layer-media simulations. In fact, the methods and studies referred in points (i) and (ii) above motivated the development of the markedly more efficient WGF alternative.</p
Windowed Green function method for the Helmholtz equation in the presence of multiply layered media
This paper presents a new methodology for the solution of problems of two- and three-dimensional acoustic scattering (and, in particular, two-dimensional electromagnetic scattering) by obstacles and defects in the presence of an arbitrary number of penetrable layers. Relying on the use of certain slow-rise windowing functions, the proposed windowed Green function approach efficiently evaluates oscillatory integrals over unbounded domains, with high accuracy, without recourse to the highly expensive Sommerfeld integrals that have typically been used to account for the effect of underlying planar multilayer structures. The proposed methodology, whose theoretical basis was presented in the recent contribution (Bruno et al. 2016 SIAM J. Appl. Math. 76, 1871–1898. (doi:10.1137/15M1033782)), is fast, accurate, flexible and easy to implement. Our numerical experiments demonstrate that the numerical errors resulting from the proposed approach decrease faster than any negative power of the window size. In a number of examples considered in this paper, the proposed method is up to thousands of times faster, for a given accuracy, than corresponding methods based on the use of Sommerfeld integrals
A windowed Green function method for elastic scattering problems on a half-space
This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by “locally-rough surfaces” (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary conditions, and in both two and three spatial dimensions. The proposed WGF method relies on an integral-equation formulation based on the free-space Green function, together with smooth operator windowing (based on a “slow-rise” windowing function) and efficient high-order singular-integration methods. The approach avoids the evaluation of the expensive layer Green function for elastic problems on a half-space, and it yields uniformly fast convergence for all incident angles. Numerical experiments for both two and three dimensional problems are presented, demonstrating the accuracy and super-algebraically fast convergence of the proposed method as the window-size grows
A Windowed Green Function method for elastic scattering problems on a half-space
This paper presents a windowed Green function (WGF) method for the numerical
solution of problems of elastic scattering by "locally-rough surfaces" (i.e.,
local perturbations of a half space), under either Dirichlet or Neumann
boundary conditions, and in both two and three spatial dimensions. The proposed
WGF method relies on an integral-equation formulation based on the free-space
Green function, together with smooth operator windowing (based on a "slow-rise"
windowing function) and efficient high-order singular-integration methods. The
approach avoids the evaluation of the expensive layer Green function for
elastic problems on a half-space, and it yields uniformly fast convergence for
all incident angles. Numerical experiments for both two and three dimensional
problems are presented, demonstrating the accuracy and super-algebraically fast
convergence of the proposed method as the window-size grows.Comment: 21 pages, 4 tables, 11 figure
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