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In this paper new stability theorems for Yee's Finite- Difference Time-Domain (FDTD) formulation are derived based on the energy method. A numerical energy expression is proposed. This numerical energy is dependent on the FDTD model's E and H field components. It is shown that if the numerical energy is bounded, then all the field components will also be bounded as the simulation proceeds. The theorems in this paper are inspired by similar results in nonlinear dynamical system. The new theorems are used to prove the stability of a FDTD model containing non-homogeneous dielectrics, perfect electric conductor (PEC) boundary, nonlinear dielectric and also linear/nonlinear lumped elements. The theorems are intended to complement the well-known Courant-Friedrich-Lewy (CFL) Criterion. Finally it is shown how the theorems can be used as a test, to determine if the formulation of new lumped element in FDTD is proper or not. A proper formulation will preserve the dynamical stability of the FDTD model. The finding reported in this paper will have implications in the manner stability analysis of FDTD algorithm is carried out in the future.

An out-of-plane coordinate transformation can avoid singular materials in a two-dimensional electromagnetic cloak. Based on numerical simulations of elliptical cylinders, in this paper we show that...

This paper presents a new method, based on the well-known method of moments (MoM), for the numerical electromagnetic analysis of scattering and radiation from metallic or dielectric structures, or both structure types in the same simulation, that are in contact with other metallic or dielectric structures. The proposed method for solving the MoM junction problem consists of two separate algorithms, one of which comprises a generalization for bodies in contact of the surface integral equation (SIE) formulations. Unlike some other published SIE generalizations in the field of computational electromagnetics, this generalization does not require duplicating unknowns on the dielectric separation surfaces. Additionally, this generalization is applicable to any ordinary single-scatterer SIE formulations employed as baseline. The other algorithm deals with enforcing boundary conditions and Kirchhoff's Law, relating the surface current flow across a junction edge. Two important features inherent to this latter algorithm consist of a mathematically compact description in matrix form, and, importantly from a software engineering point of view, an easy implementation in existing MoM codes which makes the debugging process more comprehensible. A practical example involving a real grounded monopole antenna for airplane-satellite communication is analyzed for validation purposes by comparing with precise measurements covering different electrical sizes.

This paper extends the Monte Carlo method developed in a previous paper [2] for calculating the radar backscatter from a medium of randomly distributed discrete scatterers. This extension enables the effect of multiple layers of different types of scatterers to be included in the simulations. The presence of a ground boundary is modelled by a plane lossy half-space. Results of these simulations are compared with measurements from fields of wheat and soyabean at C-band, and with calculations using radiative transfer theory.

Consider a cylindrical structure with an arbitrary core coated by a radially inhomogeneous layer in a general case. The core of the structure may be PEC, PMC, PEMC, impedance boundary, dielectric, or metamaterial. Contrary to the scattering problems of homogeneous media, scattering problems of inhomogeneous media do not have exact solutions except for special inhomogeneous profiles. In this paper, a general frequency domain method is proposed to analyze scattering from such structures on the basis of Taylor’s series concept for obliquely incident electromagnetic (EM) waves with arbitrary polarizations. The validity of the suggested method is verified by comparison with the exact solutions of some special profiles for the coating layer. Furthermore, a comparison is made between the proposed method and other commonly used methods in the literature, which confirms that the proposed method is general, fast, and has good convergence toward the solution. Moreover, as an application, we employed the method for o...

This paper considers the fast, effective imaging of a perfectly conducting crack(s) in a 2-D homogeneous medium using data measured on its boundary. Based on the structure of singular vectors of the Multi-Static Response (MSR) matrix, whose elements are normalized by a suitable test function at several frequencies, we introduce a weighted subspace migration imaging functional. Based on the relation with the Bessel functions of integer order, it is verified that this is an improved version of traditional subspace migration. Numerical experiments for small and extended cracks from noisy synthetic data support our analysis.

Electromagnetic wave scattering by a periodic array of perfectly conducting bars is studied in this paper. In the proposed approach the amplitudes of the spatial harmonics in free space above and below the array are expanded in a Fourier series with coefficients being properly chosen Legendre polynomials. As a result, the boundary and edge conditions are satisfied directly by field representation. The method results in a small system of linear equations for unknown expansion coefficients to be solved numerically. Some numerical examples are given, presenting a comparison to the mode matching technique.

A problem of electromagnetic wave scattering by a periodic parallel-plate waveguide array is studied in the paper. The scattered field above the waveguides is sought in the form of a series of spatial harmonics in accordance with the Floquet's theorem, whereas in the waveguide regions it is sought in the form of parallel plate waveguide modes. A Fourier expansion for spatial harmonics amplitudes with coefficients in the form of properly chosen Legendre functions is used to satisfy the boundary and edge conditions by field components in free space above the array. Some numerical results are given.

For studying the problem of scattering from a random medium layer with rough boundaries the radiative transfer (RT) approach is widely used. In order to better understand this procedure we compared it with the statistical wave approach. Two such wave approaches are presented in this paper: the surface scattering operator (SSO) approach, and the unified approach. In both wave approaches two conditions are essential for arriving at RT system: the ladder approximation to the intensity operator, and the quasi-stationary approximation of fields. With these approximations one arrives at the integro-differential equations of the RT system. However, to arrive at the RT boundary conditions, one has to impose further approximations. In the SSO approach weak surface correlation must be imposed. In the unified approach, one has to ignore the terms involving volumetric spectral densities, and consider only single scattering from the rough boundary when deriving the boundary conditions.

This paper presents a novel conformal FDTD technique. The time domain measured equations of invariance (MEI) is applied to truncate computational boundary by the first time in Thompson-FDTD algorithm. Since the conformal truncating boundary and conformal nodes are used, the external absorption layers for absorbing out-going wave is decreased remarkably, so the requirement of computer storage is reduced. The numerical results of two electromagnetic scattering problems validate the above conclusion.

In this paper, two approximate and efficient boundary conditions in the two dimensional Long Transmission Line-Frequency Domain (LTL-FD) circuits [1] are introduced. The first is the circuit representation of the symmetry when passing through the centers of nodes. The second is an accurate absorbing impedance boundary condition to represent open boundaries which is proved to be an efficient absorbing boundary. The validity of these conditions is first tested in the problem of radiation by a line source. The method is then applied to the problem of plane wave scattering by conducting scatterers using the null field method. A sparse banded matrix is obtained and is solved for the required scattered field. Results for square and circular conducting scatterers are given and are compared with available analytical and numerical solutions. It is found that accurate results are obtained when the distance d between the source and the outer boundary is as small as kd ≈ 1.0, where k is the wavenumber. This considera...

A new analytic method for the electromagnetic field in stratified media, the Counter-Propagation Deduction (CPD) Method, is suggested by the authors. By introducing a new concept, the Boundary Originated Set (BOS) of waves, the CPD method can directly construct the analytic solution of the EM field in an arbitrary layer, which, due to the simplicity of the deduction procedure and the expression, can be easily evaluated numerically. Taking a uniform plane wave that propagates in a horizontally stratified medium as an example, the mechanism of the method is illustrated in detail in this paper. As one of its application, the EM field in a horizontally stratified medium excited by a vertical electric dipole over it is also analyzed.

Some properties of Green's functions of waves at boundaries are presented in this paper. Of particular interest is their behaviour like Dirac delta distributions whose domain is the manifold of the boundary under consideration. We have obtained relations involving dyadic Green's functions for electromagnetic wave scattering problems with PEC, PMC and penetrable boundaries. Both isotropic and anisotropic homogeneous media are considered. Situations with multiple bodies with disjoint smooth boundaries are also part of our study. Some similar results for acoustic waves are given without proofs.

In this paper, two useful approximate boundary conditions, impedance boundary condition and resistive boundary condition, are incorporated into the newly-developed fast and accurate finite-element boundary-integral formulation for computing scattering by complex targets. Several representative numerical results are given, demonstrating the validity of this incorporated fast and accurate FE-BI formulation.

Thompson-FDTD (T-FDTD) method has been recently introduced to solving electromagnetic scatterings of irregular objects [1]. In this paper, we describe how to apply the 1st order absorption boundary condition (ABC) in the T-FDTD method to obtain more accurate solutions without increasing number of mesh layers between truncated boundary and scatterer surface. The numerical results of the scatterings for PEC circular and rectangular cylinders show effectiveness of the implement technique.

An open boundary is an unclosed surface element such as a disk, a hollow pipe of finite length, a hemisphere, and a sum of such surface elements. In this paper, on the basis of the author's rigorous mathematical theory, general algorithms to solve electromagnetic scattering by a metallic open boundary, and also by a non-metallic open boundary, are given, which enable us to solve various important problems in the study of high frequency devices such as antenna, leaky waveguide, grating, etc.

In this paper, we investigate the oscillating electromagnetic processes in a circular and regular waveguide of a moving boundary. An analytical solution for this problem is not possible in the general case. Following the suggestion in [1,2] we have developed an analytical method for the case of axisymmetric waves in the waveguide. Also the case of linearly moving boundary is treated.

The analytical study of the electromagnetic field in a circular waveguide with linearly moving boundary has been made in [1]. In this paper, we analyse the case where the argument of the LEGENDRE's associate functions is superior to 1. The W.K.B. method is used for solving this problem. The expressions of field have been determined. It is shown that the field has a modal nature and the modes are dynamics, each having an instantaneous frequency. Also a criterium of precision is given.

Several new ideas are provided for computing the spectral transverse dyadic Green's function (STDGF) of a stratified anisotropic medium in an accurate and efficient way. A modified version of the equivalent boundary method is developed which makes it possible to compute the asymptotic values of the aforementioned STDGF without employing exponential terms. This new technique for the computation of the STDGF of a stratified anisotropic medium has more numerical stability than the other techniques proposed so far, in which the use of exponential terms for the computation of the STDGF in all the range of variation of the spectral variables unavoidably leads to numerical problems for high values of the spectral variables. Also in this paper, it is shown how a two-step interpolation approach can be used for obtaining simple closed-form expressions of the STDGF of a stratified anisotropic medium in wide ranges of the spectral variables. It is expected that the use of this interpolation approach will introduce im...

One can find various mesh truncation techniques in the literature for the finite element solution of electromagnetic scattering problems. In this paper, a mesh truncation approach referred to as the three-dimensional bymoment method is considered. This approach uses two z-directed Hertz vector potentials instead of three Cartesian field components to formulate the relevant boundary conditions. The pertaining FEM field solutions are calculated by treating the scattering problem as an interior region problem. The FEM field solutions are then numerically "coupled" on a second boundary surface that is conformal to the first one and completely enclosed by it. The "coupling" procedure yields a set of expansion coefficients, with the help of which the total field solution is written as an appropriate linear combination of the interior region FEM field solutions.

In practical calculations it is often essential to truncate the computational domain by introducing artificial boundaries. The manner in which boundary conditions are approximated has an important influence on the accuracy of the results. In this paper we present a time domain technique to quantify the spurious reflection of waves from an artificial boundary, obtained by using a nonreflecting boundary condition based on rational approximations.

A hybrid combination of modal/ray-tracing and numerical techniques is developed for treating inhomogeneous or arbitrarily shaped terminations in ducts. The problem-domain, usually electrically large, is divided into two regions: one region is homogeneous and some distance away from the termination; the other one which includes the termination is (in general) inhomogeneous. A modal or ray-tracing solution is developed to solve the incoming wave in the first region, while the solution for the termination region is obtained numerically (finite differences) with an initial estimate of the boundary condition on the interface between the two regions. Then, an iterative technique, Boundary Relaxation Method (BRM), is utilized to implement the correct boundary condition. In this paper, some 2-D waveguide termination problems are analyzed to illustrate the BRM. Examples include the study of loaded waveguide cavities.

In this paper we present an overview of the two and three dimensional absorbing boundary conditions (ABCs) that can be imposed at an artificial boundary in solving open region electromagnetic scattering problems, using finite difference or finite element techniques. A listing of the different types of ABCs available in the literature is given together with a brief description of the problems being solved by imposing these boundary conditions.

Open microwave transmission line structures are analyzed in this paper in the quasi-TEM regime using the finite element method. An absorbing boundary condition (ABC) for an arbitrary outer boundary is introduced for the purpose of truncating the unbounded region surrounding the transmission line in an efficient manner. The application of the boundary condition is illustrated for three different microstrip line configurations, viz., a single line, two coupled lines, and a six-conductor line. Numerical results are compared with those published elsewhere and good agreement is found.

Finite difference methods are becoming increasingly popular in the computational electromagnetics community. A major issue in applying these methods to electromagnetic wave scattering is to limit the computational domain to a finite size, which is accomplished by selecting an outer boundary and imposing absorbing boundary conditions to simulate free space. In this paper, the pseudo-differential operator approach is employed to derive absorbing boundary conditions for both circular and elliptical outer boundaries. The pseudo-differential operator approach employed by Engquist and Majda is modified to derive improved absorbing boundary conditions. In the case of the circular outer boundary, the modified pseudo-differential operator approach leads to a condition equivalent to that of Bayliss and Turkel's second-order condition. The modified pseudo-differential operator is then used to derive the second-order absorbing boundary condition for the elliptical outer boundary. The effectiveness of the second-order...

This paper addresses TVFEM analysis of periodic structures for radiation and scattering. The basic property of TVFEM basis spaces is utilized to impose the periodic boundary condition on the opposing walls. The PMLs are used to truncate the upper and bottom boundary of a single unit cell. Numerical results are presented and compared with results obtained using alternative methods, which demonstrate the validity, accuracy and versatility of the method.

It is shown that a large class of dynamic systems with non-stationary dimensions can be solved analytically. The corresponding mathematical models of these systems are initial-boundary-value-problems for the wave equation with moving boundary conditions. The method given in a previous paper is generalized and used for solving such problems. It consists of transforming the wave equation for the domain with moving boundary into a form-invariant wave equation for a domain with fixed boundary. The transformation is accomplished through a formal change of variable, and an analytical function F(W) of a complex variable W, permitting a conformal mapping between the two domains. For the transformation to exist, F(W) has to satisfy the condition F*(W) = F(W*). We show that the solution of such systems is obtained in the form of a functional Fourier series,, and the modes are dynamical, each having an instantaneous frequency. The problem of initial conditions is also treated. Furthermore, it is shown that all possi...

The problem of radar backscattering from a vegetation layer with a smooth or a rough ground boundary is formulated by a Monte Carlo method. The vegetation layer is assumed to contain a mixture of randomly distributed dielectric discs and thin prolate ellipsoids whose phase matrices are known and whose distributions of angular orientations can be prescribed independently. The ground boundary is modelled by a Fresnel reflection coefficient for a plane lossy surface or a Kirchhoff lossy surface as the case may be. Results from the Monte Carlo simulations are compared with calculations of a matrix-doubling method by [9], and also with measurements from fields of wheat, soyabean, milo and corn [7,20]. The results indicate that the Monte Cario method presented in this paper can give a good fit with experimental data, using parameters which are believed to be reasonable.