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A symmetry relation of the integral operators in a layered medium proved by the reciprocal theory can be applied to improve the accuracy of the magnetic-field integral equation (MFIE). Based on the symmetric layered medium Green’s function, the normal vector can be transferred into the inner integral to keep the field integral as the inner integral of the elements in the impedance matrix. When discretized by the divergence-conforming function, this field-extracted scheme shows better performance than the classic expression in accuracy. Meanwhile, this form of expression can be applied in the combined-field integral equation (CFIE). Several numerical results are provided to validate the formulation of the symmetry relations from the layered medium Green’s function to the impedance matrices and to reveal its advantages in enhancing the accuracy of the field-extracted form of MFIE. [ABSTRACT FROM AUTHOR]

An efficient improved spectrum integral method (ISIM) is proposed to accelerate the scattering simulation of cuboid object by method of moment (MoM) in multiplanar layered medium (LM). The layered medium Green’s functions (LMGFs) are studied and decomposed into transmission and reflection terms, which hold the translational invariance and reverse translational invariance, respectively. By virtue of the (reverse) translational invariance of LMGF from the uniform square grids on the surface of the cuboid object, most of the coupling between the expanding basis functions and the testing basis functions can be represented by two kinds of submatrices, i.e., the Toeplitz matrix when transmission term is involved, and the conjugate Toeplitz matrix when reflection term is involved. Moreover, the submatrix coupling the expanding/testing basis functions defined on the edges with those defined on the parallel surfaces/edges is also extended to the (conjugate) Toeplitz matrixes. This will significantly alleviate the heavy computation and memory burden from the conventional SIM. With the improved operations on the basis functions associated with the edges of the cuboid object, the proposed ISIM in LM can reach the computational complexity as low as ${O}$ (${N} ^{1.5}$ log(N)) in the matrix vector production, while the computational complexity of matrix filling and the memory requirement are both ${O}$ (${N}^{1.5}$). Moreover, compared with conventional SIM, both theoretical analysis and numerical results demonstrate that the memory requirement and matrix filling time are dramatically decreased. [ABSTRACT FROM AUTHOR]

A novel electromagnetic modeling method for multidomain planar layered medium (MD-PLM) by surface integral equation (SIE) is proposed. The MD-PLM refers to the whole space that is separated into multiple PLM volumes, e.g., the infinite-sized PLM background with inserted finite PLM objects or multilayered parallel-plate structures. In the conventional SIE method for this scenario, only the exterior domain is considered as PLM that is modeled by layered medium Green’s functions (LMGFs), while the interior domain is treated by the multidomain homogeneous SIE. However, in this work, the surface equivalence formulation for this special scenario is reestablished by the LMGFs. Then, both the exterior and interior domains are considered as PLM that is modeled by the corresponding LMGFs and SIE in each subdomain. As a result, only the boundary of each sub-PLM domain is required to be discretized rather than the interfaces of each interior medium, which is different from the way in conventional SIE. Consequently, compared with the conventional SIEs, the proposed method can reduce a large quantity of unknowns and significantly increase the efficiency by reducing the memory consumption. By some numerical examples, the performance of this method is evaluated and compared with the conventional methods. The validity and efficiency of the newly proposed method are also well demonstrated in the examples. [ABSTRACT FROM AUTHOR]

The multilayered parallel-plate structure (MPPS) is a typical structure in microwave engineering. In numerical simulation, MPPS is usually modeled by an infinitely large planarly layered medium (PLM) to simplify the computation. For a realistic microwave circuit, however, the substrate is always finite in spatial extent, i.e., it is a finite-sized MPPS (FS-MPPS). To address this issue, a novel surface integral equation (SIE) formulation is proposed for the efficient simulation of FS-MPPS. In this article, the surface equivalence principle is first revisited. For the exterior and interior problems, different Green’s functions are utilized. In particular, the common homogeneous-medium Green’s function is used for the exterior homogeneous region, whereas the layered-medium Green’s function (LMGF) is applied for the interior multilayered structure. In this manner, FS-MPPS is no longer directly approximated by the infinite PLM model, but instead, it is modeled accurately by SIE whose integration kernel is derived from PLM. Finally, a PMCHWT SIE is established for the electromagnetic analysis of FS-MPPS. Due to the finite nature of the inner problem, the setting of PLM and LMGF is not unique. This nonuniqueness is studied in theory and verified by numerical simulation. It is revealed that such a nonuniqueness of the setting of the inner problem does not change the uniqueness of the final solution. To validate the proposed approach, a multidomain FS-MPPS and an FS-MPPS with embedded dielectric structures are investigated. Compared with the conventional brute-force SIE methods for FS-MPPS, where all the interfaces of the layered structure should be discretized and assigned with degrees of freedom (DOFs), the proposed method is more succinct and efficient. [ABSTRACT FROM AUTHOR]

This paper presents a novel accurate and stable current and charge integral equation (CCIE) solver for the low-frequency scattering of penetrable objects in layered medium (LM). To the best of our knowledge, this is the first time to extend CCIE into LM simulations at low frequency. In order to integrate the matrix-friendly LM Green’s functions (LMGFs) into CCIE, we have rederived them to define new quasi-vector/scalar potentials, which are able to annihilate the frequency singularity in the original LMGFs. Moreover, an effective preconditioner is adopted to improve the conditioning of impedance matrices. In comparison with other perconditioners, this method performs much better. The excellent performance of this new CCIE solver is then demonstrated by numerical experiments. [ABSTRACT FROM AUTHOR]

Accurate and efficient prediction of electromagnetic scattering from inhomogeneous objects in layered medium is one of the most challenging issues in engineering applications. This paper presents the first 3-D higher order hybrid finite-element method (FEM) and method of moments (MoM) for the accurate modeling of inhomogeneous dielectric objects in multilayered medium. The main challenges of this paper include: 1) the integration of these algorithms for layered medium and 2) the higher order computational approach involved in layered medium for high efficiency. In the proposed method, the MoM with the layered medium dyadic Green’s function is used as the exact radiation boundary condition in an inhomogeneous background, and the FEM is applied to model the inhomogeneous objects. Furthermore, the higher order maximally orthogonal basis functions with curl-conforming and divergence-conforming properties are used in the FEM and MoM, respectively to improve the modeling capability of this algorithm. For 3-D inhomogeneous objects scattering in multilayered medium, this new method requires a much more tightly truncated simulation domain than the traditional FEM, and provides much higher flexibility than the pure surface integral equation method. Finally, some numerical results are provided to validate the accuracy, efficiency, and flexibility of this method. [ABSTRACT FROM AUTHOR]