A method used to solve the problem of water waves on a sloping beach is applied to a thin conducting half plane described by a thin layer impedance boundary condition. The solution for the electric field behavior near the edge is obtained and a simple fit for this behavior is given. This field is used to determine the correction to the impedance per unit length of a conductor due to a sharp edge. The results are applied to the strip conductor. The final appendix also discusses the solution to the dual-sided (impedance surface & perfect conductor surface) half plane problem.
Capacitance/inductance corrections for grid induced errors for a thin slot models are given for both one and four point testing on a rectangular grid for surface currents surrounding the slot. In addition a formula for translating from one equivalent radius to another is given for the thin-slot transmission line model. Additional formulas useful for this slot modeling are also given.
This report examines the problem of magnetic penetration of a conductive layer, including nonlinear ferromagnetic layers, excited by an electric current filament. The electric current filament is, for example, a nearby wire excited by a lightning strike. The internal electric field and external magnetic field are determined. Numerical results are compared to various analytical approximations to help understand the physics involved in the penetration.
We provide corrections to the slot capacitance and inverse inductance per unit length for slot gasket groove geometries using an approximate conformal mapping approach. We also provide corrections for abrupt step changes in slot width along with boundary discontinuity conditions for implementation in the various slot models.
Though the method-of-moments implementation of the electric-field integral equation plays an important role in computational electromagnetics, it provides many code-verification challenges due to the different sources of numerical error and their possible interactions. Matters are further complicated by singular integrals, which arise from the presence of a Green's function. In this report, we document our research to address these issues, as well as its implementation and testing in Gemma.
Metallic enclosures are commonly used to protect electronic circuits against unwanted electromagnetic (EM) interactions. However, these enclosures may be sealed with imperfect mechanical seams or joints. These joints form narrow slots that allow external EM energy to couple into the cavity and then to the internal circuits. This coupled EM energy can severely affect circuit operations, particularly at the cavity resonance frequencies when the cavity has a high Q factor. To model these slots and the corresponding EM coupling, a thin-slot sub-cell model [1] , developed for slots in infinite ground plane and extended to numerical modeling of cavity-backed apertures, was successfully implemented in Sandia's electromagnetic code EIGER [2] and its next-generation counterpart Gemma [3]. However, this thin-slot model only considers resonances along the length of the slot. At sufficiently high frequencies, the resonances due to the slot depth must also be considered. Currently, slots must be explicitly meshed to capture these depth resonances, which can lead to low-frequency instability (due to electrically small mesh elements). Therefore, a slot sub-cell model that considers resonances in both length and depth is needed to efficiently and accurately capture the slot coupling.
In this paper, we characterize the logarithmic singularities arising in the method of moments from the Green’s function in integrals over the test domain, and we use two approaches for designing geometrically symmetric quadrature rules to integrate these singular integrands. These rules exhibit better convergence properties than quadrature rules for polynomials and, in general, lead to better accuracy with a lower number of quadrature points. In this work, we demonstrate their effectiveness for several examples encountered in both the scalar and vector potentials of the electric-field integral equation (singular, near-singular, and far interactions) as compared to the commonly employed polynomial scheme and the double Ma–Rokhlin–Wandzura (DMRW) rules, whose sample points are located asymmetrically within triangles.
Despite extensive research on symmetric polynomial quadrature rules for triangles, as well as approaches to their calculation, few studies have focused on non-polynomial functions, particularly on their integration using symmetric triangle rules. In this paper, we present two approaches to computing symmetric triangle rules for singular integrands by developing rules that can integrate arbitrary functions. The first approach is well suited for a moderate amount of points and retains much of the efficiency of polynomial quadrature rules. The second approach better addresses large amounts of points, though it is less efficient than the first approach. We demonstrate the effectiveness of both approaches on singular integrands, which can often yield relative errors two orders of magnitude less than those from polynomial quadrature rules.
We summarize the narrow slot algorithms, including the thick electrically small depth case, conductive gaskets, the deep general depth case, multiple fasteners along the length, and finally varying slot width.