Electromagnetic Boundary Value Problems Research Articles

Analyticity and uniqueness of the fractional electromagnetic boundary value problem

<abstract><p>This paper introduces a new study that examines the unique and analytical nature of the fractional solution to a fractional electromagnetic boundary value problem (BVP). This specific BVP is characterized by defining the tangential electromagnetic components. It has been proven that the analytical expressions for the fractional electromagnetic fields $ E^{\alpha} $, $ E^{*\alpha} $, $ H^{\alpha} $, and $ H^{*\alpha} $ do not vanish in any subregions $ \Omega_o^\alpha $ or $ \Omega^\alpha-\Omega_o^\alpha $. Furthermore, the unique solution makes $ E^{\alpha} = E^{*\alpha} $ and $ H^{\alpha} = H^{*\alpha} $ without singular fields at same region of the space. Analyticity of the fractional time-harmonic electromagnetic field within lossy or lossless dielectric regions is proven.</p></abstract>

Design and Simulation of a Square Loop Antenna for 920 MHz

This study describes design and simulation of a loop antenna. A square loop antenna is designed for 920 MHz. The loop antenna is then modelled and simulated using 4NEC2 electromagnetic (EM) modeling software. 4NEC2 is a completely free numerical electromagnetic modeling code. It is based on method of moments technique to solve electromagnetic boundary value problem. The 4NEC2 simulation of the loop antenna design predicted antenna resonant frequency to be 920 MHz, Return Loss bandwidth of 130 MHz and input impedance of 50.14 -j0.30 Ohm. The antenna radiation pattern is then simulated at 920 MHz. The Return Loss, VSWR, Input Impedance and Radiation Pattern of the antenna predicated by 4NEC2 simulation are studied for the possible development of copper or aluminium tube based loop antenna.

Simulation and Study of a Triangular Microstrip Patch Antenna

This study considers the simulation and study of a probe fed triangular microstrip patch antenna developed on a FR4 type substrate. The antenna design is first simulated using Sonnet Lite™ electromagnetic (EM) analysis software. Sonnet Lite™ is memory limited free version of commercial Sonnet™ electromagnetic analysis tool. It is based on method of moments technique to solve electromagnetic boundary value problem. The simulation predicted antenna resonant frequency to be 2360 MHz, Return Loss bandwidth of 36 MHz and input impedance of 52.72 Ohm. The antenna is then studied for its return loss (RL), voltage standing wave ratio (VSWR) and impedance (ZIn1) to determine its resonant frequency. The antenna resonant frequency is found to be 2380 MHz and its return loss bandwidth to be 60 MHz. The antenna radiation pattern is then measured at 2380 MHz. The RL, VSWR and ZIn1 of antenna predicated by Sonnet Lite™ are compared with their measurements which show a good agreement.

Improving radiation performance of the cylindrical dielectric reflector sandwiched by thin resistive layer illuminated by a complex line source

We studied two-dimensional (2-D) thin dielectric parabolic reflector, sandwiched by thin resistive layer from both sides. It is illuminated by an E-polarized electromagnetic plane wave from front side. It is expected to observe the radiation performance of such a composite reflector depending on the electrical and geometrical parameters. We applied two-sided generalized boundary conditions which are modified for a thin multilayer structure. The electromagnetic boundary value problem is formulated and it finally produced a set of two coupled singular integral equations (SIEs). They are handled with the analytical regularization method based on the Riemann-Hilbert Problem solution. The final numerical results are in the Fredholm second-kind matrix equation form and any desired accuracy can possibly be obtained. Also the solution procedure guarantees the convergence. It is observed that the proper selection of the electrical resistivity of the thin resistive layer produces wider bandwidth in the aperture efficiency and the directivity variation approaches to the perfect electric conductor (PEC) reflector case for higher dielectric constants. This selection can increase the allowable frequency band in the applications by coating dielectric layer from both sides. We demonstrate these statements in the numerical results section in the microwave frequency range.

Evaluation of the E‐polarization focusing ability in Thz range for microsize cylindrical parabolic reflector made of thin dielectric layer sandwiched between graphene

We consider two-dimensional (2-D) thin dielectric parabolic reflector, covered with graphene from both sides, illuminated symmetrically by an E-polarized electromagnetic plane wave. Our aim is to estimate the focussing ability of such a composite reflector depending on the graphene parameters. We use a version of the two-side generalized boundary condition, modified for a thin multilayer case. The scattering is formulated as an electromagnetic boundary-value problem; it is cast to a set of two coupled singular integral equations that are further subjected to analytical regularisation based on the known Riemann–Hilbert problem solution. Thanks to this procedure, the numerical results are computed from a Fredholm second-kind matrix equation that guarantees convergence and provides easily controlled accuracy. In the lower part of the THz range, high values of the focusing ability are observed even for a thin reflector; they are greater than for a purely dielectric reflector and a free standing graphene reflector. On the other hand, a regime of almost full transparency, intrinsic for the dielectric layer, can spoil focusing ability. Novel aspect is that the location in frequency of this effect can be controlled, in wide range, by changing the chemical potential of graphene.

Pulsed Eddy Current Testing for Electromagnetic Parameters of a Spherical Conductor

This paper provides a pulsed eddy current testing method for electromagnetic parameters of a ferromagnetic spherical conductor. Firstly, the frequency domain solution of an eddy current field to the conductor is obtained by solving the electromagnetic boundary value problem. And then the time domain expression to the induced voltage across the pickup coil excited by a pulsed current in the drive coil is calculated by inverse Laplace transform based on residue theorem. Secondly, a least squares inverse problem, between the measured and analytical values of induced voltage, is established to determine the conductivity and relative permeability of the steel ball. And the coupling relationship between the two parameters of the steel ball is explored. Thirdly, the amplitude of the excitation current is changed to study the effect on the parameter inversion results caused by detection conditions. Finally, the time domain analytical formula and the parameters inversion method are verified, by comparing the theoretical induced voltage and conductivity inversion results with experimental voltage and conductivity test values by four-point method respectively.

Well Posedness and Finite Element Approximability of Three-Dimensional Time-Harmonic Electromagnetic Problems Involving Rotating Axisymmetric Objects

A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors’ knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects.

Scattering Analysis of Modulated Corrugations in a Conducting Circular Cylinder and Study of RCS Reduction

In this communication, an electromagnetic boundary-value problem of modulated transverse corrugations in an infinite conducting circular cylinder is rigorously solved based on the Fourier transform, eigenfunction expansion, and the mode matching method. Radar cross section (RCS) of the modulated transverse corrugations is represented in the series form. Computation is performed to analyze scattering characteristics while varying depth, width, and period of the corrugations and to investigate the excitation of surface waves and concomitant RCS reduction.

Analysis of the Rigorous Coupled Wave Approach for [formula omitted]-polarized light in gratings

We study the convergence properties of the two-dimensional Rigorous Coupled Wave Approach (RCWA) for s-polarized monochromatic incident light. The RCWA is widely used to solve electromagnetic boundary-value problems where the relative permittivity varies periodically in one direction, i.e., scattering by a grating. This semi-analytical approach expands all the electromagnetic field phasors as well as the relative permittivity as Fourier series in the spatial variable along the direction of periodicity, and also replaces the relative permittivity with a stairstep approximation along the direction normal to the direction of periodicity. Thus, there is error due to Fourier truncation and also due to the approximation of grating permittivity. We prove that the RCWA is a Galerkin scheme, which allows us to employ techniques borrowed from the Finite Element Method to analyze the error. An essential tool is a Rellich identity that shows that certain continuous problems have unique solutions that depend continuously on the data with a continuity constant having explicit dependence on the relative permittivity. We prove that the RCWA converges with an increasing number of retained Fourier modes and with a finer approximation of the grating interfaces. Numerical results show that our convergence results for increasing the number of retained Fourier modes are seen in practice, while our estimates of convergence in slice thickness are pessimistic.

Dual Band RCS Reduction Using Modulated Grooves in A Conducting Plane

An electromagnetic boundary-value problem of modulated grooves in a conducting plane is rigorously solved based on the Fourier transform, eigenfunction expansion, and mode matching method. Radar cross section (RCS) of the modulated grooves is represented in a series form and calculated while varying depth, width, and period of the grooves to investigate scattering characteristics of dual band RCS reduction.

Analysis of a thin, penetrable, and non‐uniformly loaded cylindrical reflector illuminated by a complex line source

A thin, penetrable, and cylindrical reflector is illuminated by the incident field of a complex source point. The scattered field inside the reflector is not considered and its effect is modelled through a thin layer generalised boundary condition (GBC). The authors formulate the structure as an electromagnetic boundary value problem and two resultant coupled singular integral equation system of equations are solved by using regularisation techniques. The GBC provides us to simulate the thin layer better than the resistive model which is applicable only for very thin sheets. Hence, the more reliable data can be obtained for high-contrast and low-loss dielectric material. The scattering and absorption characteristics of the front-fed and offset reflectors are obtained depending on system parameters. Also, the effects of the edge loading are examined for both E- and H-polarisations. The convergence and the accuracy of the formulation are verified in reasonable computational running time.

Probability distribution of random cylinder's total scattering cross section

An arbitrary shaped scatterer is often modeled as a canonical structure while solving an electromagnetic boundary value problem. This approach approximates the boundary to provide complex analytical solutions. However, most real life structures do not have canonical or regular boundaries. Determining an analytical solution of electromagnetic scattering problem is quite a tedious task, especially for random geometries. This work proposes a method to compute the scattering statistics of a random cylinder. A formulation is developed to determine the probability density function (pdf) of scattering cross section, σT, from the statistics of random cylinder's radius. This approach eliminates the need to actually solve an electromagnetic scattering problem. The optical theorem is employed to estimate the pdf of σT from the pdf of lateral width. The proposed results are found in good agreement with the numerically simulated results.

Electro-magneto-hydrodynamic peristaltic pumping of couple stress biofluids through a complex wavy micro-channel

Biomimetic propulsion mechanisms are increasingly being explored in engineering sciences. Peristalsis is one of the most efficient of these mechanisms and offers considerable promise in microscale fluidics. Electrokinetic peristalsis has recently also stimulated significant attention. Electrical and magnetic fields also offer an excellent mode for regulating flows. Motivated by novel applications in electro-conductive microchannel transport systems, the current article investigates analytically the electromagnetic pumping of non-Newtonian aqueous electrolytes via peristaltic waves in a two-dimensional microchannel with different peristaltic waves propagating at the upper and lower channel wall (complex wavy scenario). The Stokes couple stress model is deployed to capture micro-structural characteristics of real working fluids. The unsteady two-dimensional conservation equations for mass and momentum conservation, electro-kinetic and magnetic body forces, are formulated in two dimensional Cartesian co-ordinates. The transport equations are transformed from the wave frame to the laboratory frame and the electrical field terms rendered into electrical potential terms via the Poisson-Boltzmann equation, Debye length approximation and ionic Nernst Planck equation. The dimensionless emerging linearized electro-magnetic boundary value problem is solved using integral methods. The influence of Helmholtz-Smoluchowski velocity (characteristic electro-osmotic velocity), couple stress length parameter (measure of the polarity of the fluid), Hartmann magnetic number, and electro-osmotic parameter on axial velocity, volumetric flow rate, time-averaged flow rate and streamline distribution are visualized and interpreted at length.

Shape parameter selection for multi-quadrics function method in solving electromagnetic boundary value problems

Purpose – The multi-quadrics (MQ) function is a kind of radial basis function. And the MQ method has been successfully adopted as a type of meshless method in solving electromagnetic boundary value problems. However, the accuracy of MQ interpolation or solving equations is severely influenced by shape parameter. Thus the purpose of this paper is to propose a case-independent shape parameter selection strategy from the aspect of coefficient matrix condition number analysis. Design/methodology/approach – The condition number of coefficient matrix is investigated. It is shown that the condition number is only a function of shape parameter and MQ node number, and is irrelevant to the interpolated function which means case-independent. The effective condition number which takes into account the interpolated function is introduced. Then, the relation between the relative root mean square error and condition number is analyzed. Three numerical experiments as transmission line, cable channel and grounding metal box model were carried out. Findings – In the numerical experiments, there is an approximate linear relationship between the logarithm of the condition number and shape parameter, an approximate quadratic relationship with node number. And the optimal shape parameter is corresponding to the early stage of condition number oscillation. Originality/value – This paper proposed a case-independent shape parameter selection strategy. For a finite precision computation, the upper limit of the condition number is predetermined. Therefore, the shape parameter can be chosen where condition number oscillates in early stage.

Efficient computation of the surface fields of a horizontal magnetic dipole located at the air‐ground interface

SummaryIn this paper, the classic problem of determining the fields of a vertically oriented current‐carrying small circular‐loop antenna located near a plane air–earth boundary is revisited. It is well known that the Sommerfeld integrals describing the field components generated by the loop source cannot be exactly evaluated and that their numerical integration is made difficult by the presence of highly oscillatory terms in the integrands. Here, for both source and observation points on the interface, a rigorous method is developed that allows analytical integration of the Sommerfeld integrals, providing fast‐convergent series representations for the surface fields. The obtained formulas permit to overcome all the drawbacks of the previously published approximate solutions to this problem, and to avoid the necessity of using purely numerical approaches when high computational accuracy is required. At the same time, the proposed series representations constitute an analytical benchmark for numerical procedures employed to solve electromagnetic boundary value problems, with applications in antenna design and close‐to‐the‐surface communication. Copyright © 2015 John Wiley & Sons, Ltd.

Well posedness and finite element approximability of two-dimensional time-harmonic electromagnetic problems involving non-conducting moving objects with stationary boundaries

A set of sufficient conditions for the well-posedness and the convergence of the finite element approximation of two-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting moving objects with stationary boundaries is provided for the first time to the best of authors’s knowledge. The set splits into two parts. The first of these is made up of traditional conditions, which are not restrictive for practical applications and define the usual requirements for the domain, its boundary, its subdomains and their boundaries, the boundary conditions and the constitutive parameters. The second part consists of conditions which are specific for the problems at hand. In particular, these conditions are expressed in terms of the constitutive parameters of the media involved and of the velocity field. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve axially moving media.

Simulation Analysis of Static Characteristics of CJX2-40 Type AC Contactor Electromagnetic Mechanism

At present, the finite element method has been widely used in electrical engineering; value has an absolute advantage in the field of solving the problem of position in the electromagnetic boundary. From the perspective of historical development, for solving the electromagnetic boundary value problems, four kinds of methods are used namely; graphical method, simulation method, analytical method and numerical calculation . This study introduced finite element method which has developed rapidly. Before finite element method, numerical calculation method was used, although this method was effective to a certain extent but the results showed that it had a limited range of the electromagnetic boundary value problems to be solved.

Integral Transforms in Electromagnetic Formulation

In this research, integral transform technique for electromagnetic scattering formulation is reviewed. Electromagnetic boundary-value problems are presented to demonstrate how the integral transforms are utilized in electromagnetic propagation, antennas, and electromagnetic interference/compatibility. Various canonical structures of slotted conductors are used for illustration; moreover, Fourier transform, Hankel transform, Mellin transform, Kontorovich-Lebedev transform, and Weber transform are presented. Starting from each integral transform definition, the general procedures for solving Helmholtz’s equation or Laplace’s equation for the potentials in the unbounded region are reviewed. The boundary conditions of field continuity are incorporated into particular formulations. Salient features of each integral transform technique are discussed.

Bounds on the average of total scattering cross section of random cylinder

Total scattering cross section (σT) of a PEC cylindrical scatterer is a function of it's scattering amplitude and is closely related to scatterer's cross section. It is difficult to determine σT analytically for arbitrary cross sections of scatterer, especially for random cross sections. Defining some bounds on the value of σT is therefore very helpful in its estimation. In this paper, σT of canonical shaped objects is used to define bounds on σT of random cylinder. The geometrical parameters of canonical scatterers are obtained from the geometric parameters of the random cylinder. A formulation is also developed to approximate the value of σT from its bounding values. This work therefore, helps to predict the σT of a random cylinder from its geometrical parameters, without solving an electromagnetic boundary value problem.

Refoundation of the Cell Method Using Augmented Dual Grids

In this paper, the cell method (CM) is reformulated using augmented dual grids. In this way, the boundary of the discretized spacial domain can be properly dealt with and energetic quantities can be introduced, overcoming the well-known drawbacks of the CM. The details are given for electromagnetic boundary value problems, whose discretization can severely suffer from such drawbacks of the CM.