Single-source Surface Integral Equation Research Articles

Single-Source SIE for 2-D Arbitrarily Connected Penetrable and PEC Objects With Nonconformal Meshes

We proposed a simple and efficient modular single-source surface integral equation (SS-SIE) formulation for electromagnetic analysis of arbitrarily connected penetrable and perfectly electrical conductor (PEC) objects in two-dimensional space. In this formulation, a modular equivalent model for each penetrable object consisting of the composite structure is first independently constructed through replacing it by the background medium, no matter whether it is surrounded by the background medium, other media, or partially connected objects, and enforcing an equivalent electric current density on the boundary to remain fields in the exterior region unchanged. Then, by combining all the modular models and any possible PEC objects together, an equivalent model for the composite structure can be derived. The troublesome junction handling techniques are not needed and non-conformal meshes are intrinsically supported. The proposed SS-SIE formulation is simple to implement, efficient, and flexible, which shows significant performance improvement in terms of CPU time compared with the original SS-SIE formulation and the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation. Several numerical examples including the coated dielectric cuboid, the large lossy objects, the planar layered dielectric structure, and the partially connected dielectric and PEC structure are carried out to validate its accuracy, efficiency and robustness.

Vector Single-Source Surface Integral Equation for TE Scattering From Cylindrical Multilayered Objects

A single-source surface integral equation (SS-SIE) for transverse electric (TE) scattering from cylindrical multilayered objects is proposed in this paper. By incorporating the differential surface admittance operator (DSAO) and recursively applying the surface equivalence theorem from innermost to outermost boundaries, an equivalent model with only electric current density on the outermost boundary can be obtained. In addition, an integration approach is proposed, where the small argument expansion of the Hankel function is used to evaluate the singular and nearly singular integrals. Compared with other SIEs, such as the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation, the computational expenditure is reduced for multilayered structures because only a single source is needed on the outermost boundary. As shown in the numerical results, the proposed method generates only 19% of unknowns, uses 26% of memory, and requires 29% of the CPU time of the PMCHWT formulation.

Formulation of Single-Source Surface Integral Equation for Electromagnetic Analysis of 2D Partially Connected Penetrable Objects

This paper presents a new single-source surface integral equation (SS-SIE) to model the partially contacted penetrable objects. In the proposed formulation, the surface electric and magnetic fields on all interior boundaries are first eliminated through combining integral solutions inside each object. Then, by enforcing the surface electric fields in the original and equivalent configurations are equal to each other, an equivalent model with only electric current density on the outermost boundaries is derived. Compared with other SIEs, like the PMCHWT formulation, all unknowns are residing on the outermost boundaries in the proposed formulation and therefore, less count of unknowns can be obtained. Finally, three numerical examples are carried out to validate the effectiveness of the proposed SS-SIE.

Single-Source Surface Integral Equation Formulations for Characteristic Modes of Fully Dielectric-Coated Objects

We herein propose two novel surface integral equation formulations for the characteristic modes (CMs) of fully dielectric-coated objects, including dielectric-coated metal and dielectric-coated dielectric. The proposed approaches are based on the intrinsic dependent relationships between varieties of surface currents. Compared to the early CMs formulations for dielectric-coated objects, the proposed methods can suppress redundant modes. The numerical results of two practical antennas demonstrate that the proposed approaches can accurately provide the modal behaviors of fully dielectric-coated objects, which can provide the guidelines for the antenna engineering.

Novel Single-Source Surface Integral Equation for Scattering Problems by 3-D Dielectric Objects

A new single-source integral equation is proposed for the solution of electromagnetic wave scattering problems. The traditional volume electric field integral equation is reduced to the new single-source surface integral equation by representing the electric field inside the scatterer as a superposition of spherical waves emanating from its boundary. Such new integral equation formulation has been previously developed for the scalar and vector cases of 2-D scattering problems. In this paper, the 3-D form of this new single-source surface integral equation for scattering on homogeneous nonmagnetic dielectrics is proposed. Detailed description of the method of moments (MoMs) discretization and its resultant matrices is presented. In order to validate the new integral equation formulation and verify the accuracy of its MoMs discretization, its solution is compared against the analytical Mie series solution and fields computed using the commercial electromagnetic analysis software.

New Vector Single-Source Surface Integral Equation for Scattering Problems on Dielectric Objects in 2-D

A new surface single-source integral equation (SSIE) is proposed for the solution of electromagnetic wave scattering problems in two dimensions. The traditional volume electric field integral equation (V-EFIE) is reduced to the new single-source surface integral equation by representing the electric field inside the scatterer as a superposition of cylindrical waves emanating from its boundary. While being rigorous in nature, the new single-source surface integral equation features half of the degrees of freedom compared with traditional surface integral equation formulations. It is amenable to derivative-free method of moments discretization as it features only electric-field-type of Green’s function instead of both electric and magnetic field Green’s functions.

New Single-Source Surface Integral Equation for Magneto-Quasi-Static Characterization of Transmission Lines Situated in Multilayered Media

We recently proposed a novel single-source integral equation (SSIE) for accurate broadband resistance and inductance extraction and current flow modeling in 2-D conductors. The new surface integral equation is advantageous compared with the traditional volume electric field integral equation (V-EFIE) used for the inductance extraction, since the unknown function is defined on the surface of conductors as opposed to the volumetric unknown current density in V-EFIE. The new SSIE is also more suitable for the solution of inductance extraction problems than the traditional surface integral equation formulations, as it features only a single unknown surface function as opposed to having the unknown equivalent electric and magnetic surface current densities. The new equation also features only the electric field Green’s functions unlike the previously known SSIE formulations. The latter property makes the new SSIE equation particularly suitable to the inclusion of the multilayered substrate effect into the inductance extraction model. This paper describes the generalization of the new SSIE formulation to the case of transmission line models embedded into the multilayered lossy substrates. This paper also shows how the matrix sparsity in the method of moments discretization of the novel integral equation can be exploited to accelerate its numerical solution and reduce associated memory use. This sparsity arises due to the skin-effect-based attenuation of the fields in conductors’ cross sections leading to vanishing levels of the matrix elements corresponding to the distant interactions. Typical examples of inductance extraction in complex interconnects situated in lossy substrate are considered to validate the proposed techniques against traditional approaches.

Surface–Volume–Surface Electric Field Integral Equation for Magneto-Quasi-Static Analysis of Complex 3-D Interconnects

A novel single-source surface–volume–surface integral equation is proposed for accurate broadband resistance and inductance extraction in 3-D interconnects. The new equation originates in the volume integral equation (VIE) traditionally used for magneto-quasi-static modeling of current flow in 3-D wires. The latter is reduced to a surface integral equation by representing the electric field inside each conductor segment as a superposition of cylindrical waves emanating from the conductor's boundary. As no approximation is utilized and all underlying boundary conditions and pertinent equations are satisfied in the reduction, the new integral equation is rigorously equivalent to the solution of the traditional volume electric field integral equation. The rigorous nature of the proposed single-source surface integral equation is corroborated numerically. In this paper, a detailed description of the method of moments discretization for the proposed surface integral equation is also presented. Numerical solution of the proposed surface integral equation for a 12-conductor bond-wire package is used to demonstrate the accuracy of the method and its computational benefits compared to the traditional solution based on the VIE.

New Single-Source Surface Integral Equations for Scattering on Penetrable Cylinders and Current Flow Modeling in 2-D Conductors

The traditional volume electric field integral equation (IE) used for solution of full-wave scattering problems on penetrable scatterers of arbitrary cross section and its magnetostatic counterpart commonly utilized for the resistance and inductance extraction problem are reduced to a novel derivative-free single-source surface IE. The reduction of volume to surface IE is based on representation of the electric field in the cylinder cross section in the form of a single-layer ansatz. Substitution of such surface based electric field representation into the volume IE reduces it to a surface IE with respect to the unknown surface current density. Since the new surface IE enforces exactly the field continuity at the material interfaces, the radiation condition as well as underlying Helmholtz equations both inside and outside the penetrable cylinder, it is rigorously equivalent to the solution of Maxwell's equations. The method of moments discretization of the new IE is shown to produce an error-controllable field approximation. Due to the presence of a product of surface-to-volume and volume-to-surface integral operators, the discretization of the novel surface-volume-surface IE requires both surface and volume meshes.

Reduction of Multiply-Nested Dielectric Bodies for Wave Scattering Analysis By Single Source Surface Integral Equations

A recursive single source surface integral equation formulation for the problem of electromagnetic wave scattering by multiply-nested bodies yields an equivalent outer surface model that is independent of the material and the illumination in the exterior region, and therefore invariant under rotation and translation. The proposed algorithm is applicable to both far-field and near-field problems, and also gives, through a fast backward recursion, the field values at interior points. Such a reduced model may be duplicated and reused in an assortment of complex scattering problems without repeating the reduction calculation. Thus, the high computational efficiencies realized by the recursive formulation, with respect to the previous, direct, single source surface integral equation formulations, are further enhanced for problems involving some degree of repetition, as in geometry and material optimization of scattering structures under various types of illumination. Numerical examples are included in order to demonstrate the features and the efficiency of the recursive multiply-nested algorithm in comparison to direct, simultaneous solution of all unknowns by the electric field integral equation method.

A recursive single-source surface integral equation analysis for wave scattering by heterogeneous dielectric bodies

The problem of electromagnetic wave scattering by heterogeneous dielectric bodies is formulated in a recursive manner by organizing their homogeneous subregions into hierarchical multiply-nested structures. The inner details of each multiply-nested body are completely accounted for by an equivalent surface representation that yields the electric and magnetic fields tangent to the body only in terms of a single unknown electric surface current density distributed on its outer surface. In this manner, the problem of wave scattering by heterogeneous dielectric bodies is reduced to a scattering problem over their outermost surfaces in terms of only a single unknown current density. For a large number N of different homogeneous dielectric subregions within such a heterogeneous body, the proposed method has a computational complexity of O(N/sup 1.5/) and storage requirements that increase in proportion to O(N). Furthermore, the equivalent surface representation derived for a particular subregion is invariant under rotation and translation and may, therefore, be applied to identical subregions without repeating the computation. The fields at any interior points are calculated by a fast backward recursion.