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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]

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]