2379-8793 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JMMCT.2020.2966366, IEEE Journal on Multiscale and Multiphysics Computational Techniques IEEE JOURNAL ON MULTISCALE AND MULTIPHYSICS COMPUTATIONAL TECHNIQUES, VOL. 4, NO. 12, 2019 1 Surface-Volume-Surface EFIE for Electromagnetic Analysis of 3-D Composite Dielectric Objects in Multilayered Media Reza Gholami, Student Member, IEEE, Shucheng Zheng, Student Member, IEEE, and Vladimir I. Okhmatovski, Senior Member, IEEE Abstract—The Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE) is generalized for the case of scatter- ing problems on the composite non-magnetic dielectric objects situated in planar non-magnetic layered medium. The piece- wise homogeneous regions of the scatterer can be arbitrarily positioned with respect to the layers of stratification. The SVS- EFIE being a class of single source integral equations (SSIE) is formed by restricting the surface single source electric field representation in each distinct region of the scatterer through the Volume-EFIE (V-EFIE) enforced on the boundary of that region for only the tangential component of the total field. As a result, the SVS-EFIE utilizes only the electric field dyadic Green’s functions. This allows for its cast into the mixed-potential form using classical Michalski-Zheng’s formulation and Method of Moments (MoM) discretization featuring easily computable integrals with singularities no stronger than 1/R, R being the distance from the source to the observation point in such integrals. The matrices of MoM discretization are represented in hierarchical form (as H-matrices) enabling solution of the scattering problems in multilayered media with O(N α log N ) CPU time and memory complexities, where α is a geometry dependent constant ranging from 1 to 1.5 depending on the shape of the scatterer. While the MoM surface and volume meshes discretizing the regions of the scatterer are constructed to ensure that no mesh element crosses interfaces between the layers, the clusters of both the surface and volume elements in their respective recursive partitionings in the process of H-matrix construction are allowed to span multiple layers of the medium. Upon computation of the layered medium Green’s function kernels with the Discrete Complex Image Method (DCIM) allowing clusters of elements to cross dielectric interfaces between the layers is shown to preserve compressibility of the corresponding H-matrix blocks. Index Terms—Boundary element method, composite objects, electromagnetic analysis, multilayered media, method of moments (MoM), single source integral equations. I. I NTRODUCTION Analysis of electromagnetic fields in the presence of general objects situated in multilayered media has been of signif- icant interest and topic of intensive research over several decades [1], [2]. This interest is fuelled by a broad variety Manuscript received Sept. 3, 2019; The work was supported by the Discovery Grant from Natural Sciences and Engineering Research Council (NSERC). The authors are with the Department of Electrical and Com- puter Engineering, University of Manitoba, Winnipeg, R3T 5V6 MB, Canada (e-mail: gholamir@myumanitoba.ca, umzheng6@myumanitoba.ca, vladimir.okhmatovski@umanitoba.ca). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier of applications in both science and engineering ranging from nanotechnology to geoscience, in which such analysis plays a critical role. Scattering of light on quantum dots deposited in photonic crystal slabs [3], signal propagation on high-speed interconnects [4], transient analysis of power installations and their grounding systems [5], and scattering on undergrounds reservoirs of oil and gas [6] are just few such applications. Analysis techniques based on direct solution of the differ- ential equations of electromagnetics such as Finite Element Method (FEM) [7] and Finite-Difference Method (FDM) [8] and based on solution of the integral equations [9] exist for field problems in multilayered media. While the FEM and FD techniques offer great flexibility in handling complex geometries and material properties of the objects and result in sparse matrix equations, they struggle with handling thin layers, accumulation of error when structures span electrically large areas, large number of involved degrees of freedom due to the need to discretize both layers and the objects, and perturbation of the sought fields due to truncation of the mesh. The integral equation formulations are free from the above issues. However, they result in dense matrix equations which call for use of sophisticated fast algorithms to afford solution of practically interesting problems. They are also limited in their ability to handle complex materials featuring anisotropy and inhomogeneities. Despite these limitations the integral equation methods have been the methods of choice for analyzing the fields in the layered media. The primary reason for this is the ability of the integral equations to decompose the problem into the problem of finding the field of point source in the presence of the layers (a.k.a. the Green’s function [10]) and the problem of finding unknown fields in the object itself. Analogously with the integral equations formulated for the penetrable objects situated in free space, the integral equations for the objects situated in multilayered media can be stated with respect to the distribution of unknown fields in the objects’ volume (volume integral equations, VIEs [1], [11]), with respect to the tangential components of the electric and magnetic field on the object’s boundary (traditional surface integral equations, SIEs [12]–[15]), or with respect to a single unknown vector function defined on the object’s surface and acting as the weighting function for the waves emanating from its points (single source surface integral equations, SSSIEs [16]–[20]). The SSSIE have the least degrees of freedom upon MoM discretization out of the three classes of equations. They also offer simple handling of the material