Mixed-potential Electric Field Integral Equation Research Articles

Efficient numerical analysis of finite FSS with multilayered media by MLACA

In this study, an efficient numerical technique for transmission characteristic analysis of finite planar frequency selective surface (FSS) with multilayered media is presented by using the multilevel adaptive cross approximation (MLACA). The computational scheme is based on the mixed-potential electric field integral equation (MPIE) with multilayered media Green's functions (MLGFs). The three-level modified discrete complex images method (DCIM) is presented for the spatial-domain MLGFs without any quasi-static and surface-wave extraction. For electrically large-size FSS structures, the MLACA method is then employed to alleviate the high computational complexity and memory requirement of method of moments. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.

Exact Relationship Between the Locally Corrected Nyström Scheme and RWG Moment Method for the Mixed-Potential Integral Equation

The exact relationship between the Rao–Wilton–Glisson (RWG) method of moments (MoM) and the locally corrected Nystrom (LCN) method for the mixed-potential (MP) electric field integral equation (EFIE) is presented as an extension to our work where we established analogous exact relationship for solving the EFIE in its vector-potential (VP) form. It is shown that in order to achieve one such relationship for the MP EFIE, the first- and zeroth-order LCN methods must be, respectively, used for the discretization of the VP and scalar-potential terms of the MP EFIE. The resulting numerical scheme is a point-based RWG MoM discretization of the MP EFIE via the Nystrom method. Due to the MP formulation of the EFIE, the proposed method establishes notably higher accuracy compared to either RWG MoM or LCN discretizations of the EFIE in the VP form. The increased accuracy is attributed to the analytical cancellation of the line charge contributions in the MP formulation as opposed to numerical cancellation inherent in the VP formulation of the EFIE. The detailed study and explanations of the above cancellations is presented along with their impact on the accuracy of the respective schemes for both canonical and realistic scattering targets at different frequencies.

Application of DCIM on Marine Controlled-Source Electromagnetic Survey

The discrete complex image method (DCIM) is used to calculate the mixed-potential electric field integral equation. The DCIM has been used broadly in high-frequency domain, and now is successfully introduced to the extremely low-frequency situation of marine controlled-source electromagnetic (MCSEM) survey. The integral path in high-frequency situation does not hold valid for extremely low-frequency situation. The reason can be ascribed to the change of wave number formulas. A new integral path suitable for the extremely low-frequency situation is proposed. The appropriate ranges of the parameters used in DCIM are given. The computation is stable at these considerably large ranges. The results of a five-layer model calculated with DCIM are compared with those with the filter method and the direct integral method. The computation time with DCIM is comparable to the time with filter method. The effects of water depth, upper-sediment thickness, and oil-layer thickness are studied with DCIM. The results show that electric field varies with the change of thickness. The effects accord to the physical meanings of MCSEM survey. It is safe to conclude that the DCIM with the new path is valid in MCSEM survey.

A Systematic Coupled Approach for Electromagnetic Susceptibility Analysis of a Shielded Device With Multilayer Circuitry

This paper presents a systematic coupled approach for electromagnetic susceptibility (EMS) analysis of a shielded electronic device in the presence of an ambient electromagnetic interference (EMI). A full-wave electromagnetic modeling technique coupled with a circuit-based method is developed for the overall EMS performance analysis. The mixed-potential electric field integral equation (MPIE) is formulated via the method of moments to model the electromagnetic properties of an arbitrary structure consisting of wires and surfaces with any applied excitation. With numerical analysis, the effect of an ambient electromagnetic noise is characterized, and an equivalent circuit model is extracted for further analysis of EMI to internal high-speed sensitive circuits. Numerous examinations exhibit that this systematic coupled approach is a computationally efficient method to address the EMS problems at system level, in which the external EMI effects are fully considered and the circuit-based simulator is also exploited.

Fast full-wave analysis of multistrip transmission lines based on MPIE and complex image theory

The mixed-potential electric-field integral equation is used in conjunction with the Galerkin's method and complex image theory for analyzing a transmission line with multiple strips embedded in different layers of a multilayered uniaxially anisotropic dielectric substrate. The two-dimensional Green's functions for the scalar and vector potentials are analytically obtained in the space domain due to the approximation of its spectral-domain version with complex images, thus avoiding lengthy numerical evaluations. Double integrals involved in the computation of Galerkin's matrix entries are quasi-analytically carried out for the chosen basis functions, which are well suited to the problem.

Transient currents on lightning protection systems due to the indirect lightning effect

A general efficient method for analysing transient currents on lightning-control installations for protecting various structures (buildings) against lightning electromagnetic pulse (LEMP) effects is presented. The method is based upon the frequency-domain mixed-potential electric field integral equation formulation combined with the method of moments and the Fourier transform technique. Attention is focused on predicting the indirect effects of LEMP. The transmission-line representation of lightning return stroke, and the double exponential pulse model for the current at the channel base are employed in LEMP calculation. Several example problems are considered to illustrate the capability of the method. Some theoretical results are compared with experimental data obtained from measurements on the reduced-size models of lightning protection systems.

Analysis of multiconductor transmission lines of arbitrary cross section in multilayered uniaxial media

A mixed-potential electric field integral equation is formulated and applied in conjunction with the method of moments to analyze a transmission-line system consisting of multiple conducting strips of arbitrary cross section embedded in a stratified medium with or without top and/or bottom ground planes. Each layer of the medium is possibly uniaxially anisotropic, with its optical axis perpendicular to the dielectric interfaces. Computed dispersion curves and modal currents are presented and, when possible, are compared with data available in the literature. >

Transverse electric wave scattering by two‐dimensional surfaces of arbitrary shape in the presence of a wedge

Two forms of the so‐called mixed‐potential electric field integral equation (MPIE) are developed for two‐dimensional, perfectly conducting (PC) surfaces of arbitrary shape in the presence of an infinite, PC wedge, subject to transverse electric excitation. One of the MPIEs is based on the Coulomb gauge while the other employs the Lorentz gauge. In either case the effect of the wedge is incorporated in the integral equation by means of the appropriate Green's functions, leaving the current distribution on the arbitrary surface as the only unknown. The Green's functions are derived by the eigenfunction expansion technique. A well‐established moment method procedure is adapted to numerically solve both forms of the MPIE. Computed results are presented for several cases of interest, and the relative merits of the Coulomb and Lorentz gauge MPIEs are discussed.

Comparison of Lorentz and Coulomb gauge formulations for transverse-electric wave scattering by two-dimensional surfaces of arbitrary shape in the presence of a circular cylinder

Two forms of the so-called mixed-potential electric field integral equation (MPIE) are developed for two-dimensional perfectly conducting (PC) surfaces of arbitrary shape in the presence of an infinite PC cylinder of circular cross section subject to transverse-electric (TE) excitation. One of the MPIEs is based on the Coulomb gauge; the other uses the Lorentz gauge. In either case, the effect of the cylinder is incorporated in the integral equation by means of the appropriate Green's functions, leaving the current distribution on the arbitrary surface as the only unknown. The Green's functions are derived by the eigenfunction expansion technique. An existing well-established moment method procedure is adapted to solve both forms of the MPIE numerically. Computed results are presented for several cases of interest, and the relative merits of the Coulomb and Lorentz gauge MPIEs are discussed. >

Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media. I. Theory

An accurate and general procedure for the analysis of electromagnetic radiation and scattering by perfectly conducting objects of arbitrary shape embedded in a medium consisting of an arbitrary number of planar dielectric layers is developed. The key step in this procedure is a formulation of the so-called mixed-potential electric field integral equation (MPIE) that is amenable to an existing advanced solution technique developed for objects in free space and that employs the method of moments in conjunction with a triangular-patch model of the arbitrary surface. Hence, the goal is to immediately increase analysis capabilities in electromagnetics, yet remain compatible with the large existing base of knowledge concerning the solution of surface integral equations. Three alternative forms of the MPIE in plane-stratified media are developed, and their properties are discussed. One of the developed MPIEs is used to analyze scatterers and antennas of arbitrary shape that penetrate the interface between contiguous dielectric half-spaces. >

On the scalar potential of a point charge associated with a time-harmonic dipole in a layered medium

It is demonstrated that one can choose the form of the magnetic vector potential to render the scalar potential of a single point charge associated with a horizontal, time-harmonic dipole in a layered medium identical to that associated with a vertical dipole, provided that the source and observation points are within the same layer. This proves the existence of the so-called mixed-potential electric field integral equation for objects of arbitrary shape in layered media.