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.
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 Gr…
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 Müller 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 met…
This paper introduces a novel boundary integral equation (BIE) method for the numerical solution of problems of planewave scattering by periodic line arrays of two-dimensional penetrable obstacles. Our approach is built upon a direct BIE formulation that leverages the simplicity of the free-space Green function but in turn entails evaluation of integrals over the unit-cell boundaries. Such integrals are here treated via the window Green function method. The windowing approximation together with a finite-rank operator correction -- used to properly impose the Rayleigh radiation condition -- yie…
We discuss the application of Complex-Plane Gauss-Laguerre Quadrature (CGLQ) to efficiently evaluate two-dimensional Fourier integrals arising as the solution to electromagnetic fields radiated by elementary dipole antennas embedded within planar-layered media with arbitrary material parameters. More specifically, we apply CGLQ to the long-standing problem of rapidly and efficiently evaluating the semi-infinite length "tails" of the Fourier integral path while simultaneously and robustly guaranteeing absolute, exponential convergence of the field solution despite diversity in the doubly anisot…
Efficient Green's function evaluation in layered media is a holy-grail of wave theory in general and for electromagnetics in particular. While there is a very large amount of knowledge in this context with vast literature, there are yet challenging cases such as the Green's function in thick lossy media and the Green's function at thick media with negative parameters. Here we propose a technique that can nicely tackle these issues. Our approach is based on a rational function approximation of the spectra using the Fourier-Padé approximation that is carried out in a conformal mapped spectral pl…
Pseudo-spectral frequency-domain method with background field decomposition and Green's function preconditioner for electromagnetic scattering problem in EUV lithography
Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequencies
MIT（麻省理工学院）；Pontificia Universidad Católica de Chile（智利天主教 Pontificia 大学）；Louisiana State University（路易斯安那州立大学）；New Jersey Inst. of Technology（新泽西理工学院）；Duke University（杜克大学）
On the surface plasmonic waves excited by a dipole above anisotropic and spatially dispersive two-dimensional surfaces of infinite extent in planarly layered media
Anisotropic and spatially dispersive graphene patches of arbitrary shape embedded in planarly layered uniaxial media are analyzed using spectral-domain method of moments. Formulation and computational methods for the spectral-domain method of moments using the Rao-Wilton-Glisson subdomain basis function and incorporating the full-wavevector Bhatnagar-Gross-Krook formulation of graphene surface conductivity tensor are proposed. The impedance matrix is efficiently evaluated by a novel numerical method which firstly approximates the spectral-domain Green function, basis function and conductivity …
Convolution quadrature methods for time-domain scattering from unbounded penetrable interfaces
Institute for Mathematical and Computational Engineering, School of Engineering and Faculty of Mathematics, Pontificia Universidad Católica de Chile（智利天主教大学工程学院与数学学院计算与数学工程研究所）；Department of Mathematics, Massachusetts Institute of Technology（麻省理工学院数学系）
A Uniformly High-Accuracy PML-BIE Method for Scattering by Periodic Arrays of Obstacles: The 2D Case
University of Electronic Science and Technology of China（电子科技大学）；University of Twente（特温特大学）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
The boundary element method (BEM) enables the efficient electromagnetic modelling of lossy conductors with a surface-based discretization. Existing BEM techniques for conductor modelling require either expensive dual basis functions or the use of both single- and double-layer potential operators to obtain a well-conditioned system matrix. The associated computational cost is particularly significant when conductors are embedded in stratified media, and the expensive multilayer Green's function (MGF) must be invoked. In this work, a novel single-source BEM formulation is proposed, which leads t…
A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM formulations either lead to a poorly conditioned system matrix for multiscale problems, or are computationally expensive for objects embedded in layered substrates. This article presents a new BEM formulation which leverages the surface equivalence principle and Buffa-Christiansen basis functions defined on a dual mesh, to obtain a well-conditioned system ma…
