Electromagnetic Fields In Inhomogeneous Media Research Articles

CALCULATION OF ELECTROMAGNETIC FIELDS IN INHOMOGENEOUS MEDIA FOR SELECTION OF PROTECTIVE COATINGS

The aim of the work is to develop a method for high-frequency EMFs calculation in terms of the modified vector potential and to use it for choice of the parameters of the layered absorbing coatings that provide effective absorption of radio wave radiation. Methodology. A method for calculation of electromagnetic fields in inhomogeneous media is described. It is performed in terms of the modified magnetic potential at presented a plane electromagnetic wave as an incident and reflected one. To reduce the computational domain size, additional uniaxially perfectly matched layers ensuring fast and non-reflective attenuation of electromagnetic field (EMF) strengths are used at its boundaries. It is supposed that electrical parameters of such layers have not only resistive, but also magnetic losses. Results. Modification of the known methods for dividing the wave into the incident and reflected, as well as introducing uniaxially perfectly matched layers at the domain boundaries and formulation of the problem in terms of the modified vector potential, provide a possibility to solve the problem of the electromagnetic wave incidence onto heterogeneous media at reduced memory and counting time compared to the formulation tasks through the EMF strengths. Practical value. The described method was used to select parameters of radio-absorbing coatings, application of which on conductive bodies reduces the reflections from them of the incident electromagnetic waves. This provides a possibility to choose the electrical parameters of layered coatings with active losses, as well as magnetic losses, which provide a decrease of the reflected waves amplitude by an order of magnitude or more. Originality. For the first time, the problem of calculating the incidence of an electromagnetic wave on an inhomogeneous medium with active electrical and magnetic losses was formulated in terms of the modified vector potential. The parameters of a multilayer lossy coating, which ensures decrease of the reflected EMF wave strengths by an order of magnitude or more are determined.

A Comparison of Two Numerical Mode-Matching Methodologies for the Analysis of Inhomogeneous Media With Radial and Vertical Stratifications

The numerical mode-matching (NMM) technique is a very efficient method to solving field problems in inhomogeneous media. In particular, NMM is well suited for the analysis of electromagnetic well-logging sensors for geophysical prospecting. In this communication, we compare two recent NMM strategies that have yielded higher efficiency in the analysis of electromagnetic fields in inhomogeneous media with radial and vertical stratifications. We present numerical results for three test scenarios that demonstrate the resulting improvements in the modeling of typical well-logging tools used for oil and gas explorations.

Modulated electromagnetic fields in inhomogeneous media, hyperbolic pseudoanalytic functions, and transmutations

The time-dependent Maxwell system describing electromagnetic wave propagation in inhomogeneous isotropic media in the one-dimensional case reduces to a Vekua-type equation for bicomplex-valued functions of a hyperbolic variable, see Kravchenko and Ramirez [Adv. Appl. Cliord Algebr. 21(3), 547–559 (2011)]. Using this relation, we solve the problem of the transmission through an inhomogeneous layer of a normally incident electromagnetic time-dependent plane wave. The solution is written in terms of a pair of Darboux-associated transmutation operators [Kravchenko, V. V. and Torba, S. M., J. Phys. A: Math. Theor. 45, 075201 (2012)], and combined with the recent results on their construction [Kravchenko, V. V. and Torba, S. M., Complex Anal. Oper. Theory 9, 379-429 (2015); Kravchenko, V. V. and Torba, S. M., J. Comput. Appl. Math. 275, 1–26 (2015)] can be used for efficient computation of the transmitted modulated signals. We develop the corresponding numerical method and illustrate its performance with examples.

Analytic solutions of electromagnetic fields in inhomogeneous media

We present guidelines for teaching students how to analytically solve problems that involve inhomogeneous media in electrostatic fields, stationary current fields, and stationary magnetic fields. At the introductory level, the focus is on recognizing classes of problems that can be solved in closed form and applying simple rules, based on comparison with solutions in homogeneous media. At the intermediate level, the focus is on strict proofs based on vector calculus.

Analysis of Electromagnetic Fields in Inhomogeneous Media by Fourier Series Expansion Methods--The Case of a Dielectric Constant Mixed a Positive and Negative Regions--

In this paper, we propose a new method for the electromagnetic fields with inhomogeneous media mixed a positive and negative regions by the combination of improved Fourier series expansion method using the extrapolation method which obtains the correct value of the eigenvalue and eigenvectors for the case of TM wave. Numerical results are given for the power reflection and transmission coefficient, the energy absorption, the electromagnetic fields, and the power flow in the inhomogeneous medium mixed the positive and negative regions including the case when the permittivity profiles touches zero for the TM wave. The results of our method are in good agreement with exact solution which is obtained the modified multilayer approximation method.

A finite-element method for the modeling of electromagnetic fields using generalized Cartesian elements

This paper presents a new finite-element method for the modeling of three-dimensional electromagnetic fields in inhomogeneous media. For the accurate and efficient modeling of the field along interfaces between media with different constitutive parameters, the family of generalized Cartesian finite elements is applied, that replaces the commonly used edge elements. A simple numerical example demonstrating the use of generalized Cartesian finite-elements, when applied to stationary magnetic fields, is presented.

PPP method for analysis of electromagnetic fields in inhomogeneous media

A perturbation/iterative method (the PPP method) is proposed for the analysis of electromagnetic fields in inhomogeneous media. It consists of increasing the values of the parameters the medium at all points in small increments, starting from their vacuum values, and computing the induced sources by means of the total field (the incident field, plus that of the induced sources as obtained in the preceding step). Thus, in all the perturbation/iterative steps the total excitation field is known, and therefore the solution of any problem using the method is based solely on the expression for the field of an elemental source in a vacuum. The method appears to be very versatile, conceptually the simplest possible and remarkably rapid. It also has extremely low memory requirements even for very large problems, provided that computing time is not critical. In addition, it can be combined very efficiently with other available methods, e.g. with the method of moments for the analysis of conducting antennas in a vacuum to analyse such antennas in the presence of arbitrary dielectric or magnetic bodies.

Finite‐element modeling of three‐dimensional electromagnetic fields in inhomogeneous media

An efficient and accurate finite‐element method is presented for computing three‐dimensional time‐harmonic electromagnetic fields in strongly inhomogeneous, (an)isotropic media such as are encountered in the human body, subsurface structures of the Earth, and many engineering applications. For this purpose, two types of elements are used. In the domain of computation the corresponding program decides locally what type of element has to be used for obtaining the user‐specified accuracy of modeling the field. In this way, optimum results are obtained both as regards computational efficiency and as regards desired accuracy. A method is introduced for imposing the divergence condition in a weighted sense. Numerical results are presented that demonstrate our approach to be efficient as well as accurate.

Generalized coupled azimuthal potentials for electromagnetic fields in inhomogeneous media

The original coupled azimuthal potential (CAP) formulation utilized two continuous potentials to represent the Fourier azimuthal modes of the vector field components in inhomogeneous axisymmetric material media. This formulation has since been used as the basis for finite-element solutions of radiation, scattering, and penetration problems. A generalization of the CAP formulation is presented that removes the restriction to axisymmetry of the inhomogeneous media while retaining the advantage of vector field generation in terms of only two scalar potentials. The discrete form of this generating relation is cast into a matrix transport equation, which is solved by the use of natural basis function. Variational and Galerkin approaches are considered for the solution of the given potentials. Computational examples, using finite elements, are given for the case of a simple three-dimensional boundary-value problem. >

Optimum choice of finite elements for computing three-dimensional electromagnetic fields in inhomogeneous media

A finite-element method is presented that has been specially designed for the computer modeling of three-dimensional time-harmonic electromagnetic fields in arbitrarily inhomogeneous media. For this purpose, two types of elements have been constructed. In the domain of computation the corresponding program decides locally what type of element to use for obtaining the best results as regards both computational efficiency and accuracy. Numerical results are presented that demonstrate the method to be efficient as well as accurate. >

A finite-element method for computing three-dimensional electromagnetic fields in inhomogeneous media

A finite-element method is presented that is particularly suited for the computer modeling of three-dimensional electromagnetic fields in inhomogeneous media. It employs a new type of linear vectorial expansion functions. Across an interface where the constitutive coefficients are discontinuous, they have the following properties: (1) the continuity of the tangential components of the electric and the magnetic field strengths is exactly preserved, (2) the normal component of the electric and the magnetic field strengths are allowed to jump and (3) the electric and the magnetic fluxes are continuous within the pertaining degree of approximation. The system of equations from which the expansion coefficients are obtained is generated by applying a Galerkin-type weighted-residual method. Numerical experiments are described that illustrate the efficiency of our elements, and the computational costs of the method.

Analysis of electromagnetic fields in inhomogeneous media by fourier series expansion methods

AbstractThis paper presents a new method of analysis with numerical results for planewave scattering by a layer with inhomogeneous permittivity μ(x) and permeability (x). the analysis is based on the following idea: (1) we construct a periodic structure, an iteration of the given layer and apply Maxwell's equation to derive a differential equation for this structure; (2) the electromagnetic fields in this periodic structure are expanded into Fourier series, and the obtained characteristic equation is transformed into an eigenvalue equation; (3) the electromagnetic field in the original inhomogeneous layer is expanded by the solutions of the eigenvalue equation, and the reflected and the transmitted waves are computed by using the boundary conditions. We call this method the Fourier series expansion method (FEM). When the differential equation obtained in the first step of FEM contains dϵp (x)/dx (or dμp(x)/dx), Hill's matrix method cannot be applied for the profile for which d2μp(x)/dx2 (or d2ϵp(x)/dx2) is discontinuous. By contrast, FEM in this paper can be applied even if ϵp(x) (or μp(x) is continuous. dϵp(x)/dx (or dϵp (x)/dx) is discontinuous. Even if ϵ(x) (or μ(x)) of the original inhomogeneous layer is discontinuous we can always construct a periodic structure with continuous ϵ(x) (or μ(x)), so that FEM can be applied. By numerical analysis, the usefulness of the method is evaluated from the viewpoints of the accuracy of the solution vs. the number of terms in the expansion of the comparison with already reported results. As an example of application, reflectivity is computed for the concrete layer with inhomogeneous permittivity and permeability containing magnetic particles.

Some comments on the analysis of electromagnetic fields in inhomogeneous media

AbstractAmong the principal approaches to electromagnetic field analysis in an homogeneous medium are numerical methods. The homogeneous multilayer approximation used in numerical methods is invalid when there is wave equation singularity. This paper demonstrates that the finite difference method is equivalent to the homogeneous multilayer approximation methods when the number of subdivision is increased; further, it is shown that finite difference methods also can be invalid. To analyze electromagnetic fields in the medium for which the wave equation contains a singularity, we propose here an inhomogeneous multilayer approximation method (a piecewise linear approximation) based on the power series solutions. A technique is presented for improving the homogeneous multilayer approximation method and the finite difference method by using the results of piecewise linear approximations. We further propose a modified multilayer approximation method by combining advantages of various methods. The principal features of the modified multilayer approximation method are as follows: 1) Calculations are possible even when the wave equation has several singularities; 2) the method is applicable to the structure with arbitrary medium profile; 3) the solution near the singularities can be obtained relatively easily; 4) a desired degree of accuracy can be obtained by increasing the number of subsections; and 5) no extensive mathematical background is required.The modified multilayer approximation method is used to analyze the reflection of a plane wave from an inhomogeneous plasma slab. Presented in graphical manner are the power reflection coefficient, the energy absorption, the electromagnetic field distribution inside the slab and the power flow.

Numerical modelling of geoelectric structures using the galerkin and finite elements methods

The Galerkin and finite elements methods are used to model numerically H- and E-polarized electromagnetic fields in inhomogeneous media. The error of approximation is studied and an example of numerical results is given.