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The translation matrix ($T$ -matrix) solution to the 3-D problem of scattering of the electromagnetic waves from a dielectric layered medium with random rough interfaces is presented. The solution is based on the coupled vector integral equation of the electric field using the dyadic periodic Green’s function as a kernel. It is shown that the $T$ -matrix solution conserves energy, the bistatic scattering pattern is regular even in cases, where guided modes within the layered medium are excited, and also that the method’s results coincide with those of the second-order Small Perturbation Method (SPM2) in the small height limit. One of the advantages of the $T$ -matrix method compared to the SPM2 is the wide validity range of the solution, which is also studied. [ABSTRACT FROM AUTHOR]

This paper presents a new methodology for the solution of problems of two- and threedimensional 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. [ABSTRACT FROM AUTHOR]

We present a fast direct solver for two-dimensional scattering problems, where an incident wave impinges on a penetrable medium with compact support. We represent the scattered field using a volume potential whose kernel is the outgoing Green's function for the exterior domain. Inserting this representation into the governing partial differential equation, we obtain an integral equation of Lippmann{Schwinger type. The principal contribution here is the development of an automatically adaptive, high-order accurate discretization based on a quad-tree data structure which provides rapid access to arbitrary elements of the discretized system matrix. This permits the straightforward application of state-of-the-art algorithms for constructing compressed versions of the solution operator. These solvers typically require O(N3/2) work, where N denotes the number of degrees of freedom. We demonstrate the performance of the method for a variety of problems in both low and high frequency regimes. [ABSTRACT FROM AUTHOR]

Numerical solutions for electromagnetic (EM) integral equations rely on the discretization of integral domains and the use of meshes for geometric description. Meshing geometries is very tedious, especially for complicated structures with many details (tiny parts) and geometric discontinuities (corners or edges), and remeshing could be required in many scenarios. To reduce the costs of generating quality meshes, meshless or mesh-free methods were developed and they have been extensively studied in mechanical engineering though there are less obvious interests in EM community. The meshless methods employ discrete nodes to replace meshes in the description of geometries but the background meshes for integrations are still needed traditionally. In this work, we first address the traditional meshless scheme for solving EM integral equations based on the moving least square (MLS) approximation for unknown currents and the use of background meshes for integrations, and then develop a novel meshless scheme by applying the Green's lemma to the EM surface integral equations with flat domains. The novel scheme transforms a surface integral over a flat domain into a line integral along its boundaries when excluding a singular patch in the domain. Since only the domain boundaries are discretized and no background meshes are needed, the scheme is truly meshless. Numerical examples for EM scattering by flat-surface objects are presented to demonstrate the effectiveness of the novel scheme. [ABSTRACT FROM PUBLISHER]

An integral equation‐based nonoverlapping domain decomposition method (IE‐NDDM) is proposed for efficient and accurate scattering analysis of electrically large PEC targets in a half‐space environment. Taking the condition that there are null fields as well as current inside PEC objects in the original problem, a novel explicit transmission condition is proposed to ensure continuity of electric currents between adjacent subdomains. Moreover, to deal with this situation that targets located in half‐space environment, the stratified‐medium dyadic Green's function is adopted. Numerical examples are provided to demonstrate the correctness and the performance of the proposed method. In detail, an analysis about electromagnetic scattering respect to the altitude of the target away from half‐space interface, the incident direction of plane wave, and the material parameters of the lower half‐space is presented; furthermore, the convergence behavior of the proposed method is studied. [ABSTRACT FROM AUTHOR]