一种求解三维抛物方程的迭代方法

为了高效且高精度地求解三维抛物方程(parabolic equation,PE),提出了一种求解三维PE的迭代方法.该方法采用有限差分（finite difference,FD）近似方法,保留交替方向隐式（alternating direction implicit, ADI）方法的计算模式.推导了该方法对应的相对误差关系式,在推导过程中考虑计算式分裂项丢失带来的误差影响.对比现有的求解三维PE的ADI方法 (记为ADI-PE)和克兰克·尼科森(Crank-Nicolson)求解方法 (记为CN-PE),该方法能够提高计算精准度,且可通过迭代达到一定计算精度.该方法保留了ADI的计算高效特性,是一种求解三维PE的高效高精准度的方法.     

Modeling High Frequency Propagation in Tunnel Environments by Iterative Physical Optics Method

A new formulation of the Iterative PhysicalOptics (IPO) method, including waveguide wall loss effects, hasbeen developed to model high frequency electromagnetic wavepropagation in tunnel environments. The lossy behavior of thetunnel walls has been considered throughout the inclusion of theImpedance Boundary Condition (IBC) model in the formulation of theIPO. Different arched tunnels have been studied, showing that thisapproach has a convergent behavior and providing accurate resultsfor realistic tunnel models. Moreover, the computational costassociated with the analysis of long tunnels has been significantlyreduced by using a connection scheme which splits the tunnel into aset of short sections that can be more easily analyzed. Someresults are shown, illustrating the capability of the proposedmethod.     

The use of surface impedance concepts in the finite-differencetime-domain method

Surface impedance concepts are introduced into the finite-difference time-domain (FDTD) method. Lossy conductors are replaced by surface impedance boundary conditions (SIBC), reducing the solution space and producing significant computational savings. Specifically, a SIBC is developed to replace a lossy dielectric half-space. An efficient implementation of this FDTD-SIBC based on the recursive properties of convolution with exponentials is presented. Finally, three problems are studied to illustrate the accuracy of the FDTD-SIBC formulation: a plane wave incident on a lossy dielectric half-space, a line current over a lossy dielectric half-space, and wave propagation in a parallel-plate waveguide with lossy walls     

3D parabolic equation model of EM wave propagation in tunnels

To describe radio wave propagation in curved oversized lossy waveguides of arbitrary cross-section, a vectorial parabolic equation (PE) has been derived and applied to modelling UHF/VHF radio communication in tunnels. Numerical results are presented for curved tunnels with rectangular cross-section.     

Scattering by arbitrarily cross-sectioned layered, lossy dielectric cylinders

The scattering properties of TM or TE illuminated lossy dielectric cylinders of arbitrary cross section are analyzed by the surface integral equation techniques. The surface integral equations are formulated via Maxwell's equations, Green's theorem, and the boundary conditions. The unknown surface fields on the boundaries are then calculated by flat-pulse expansion and point matching. Once the surface fields are found, scattered field in the far-zone and radar cross section (RCS) are readily determined. RCS thus obtained for circular homogeneous dielectric cylinders and dielectric coated conducting cylinders are found to have excellent agreements with the exact eigenfunction expansion results. Extension to arbitrary cross-sectioned cylinders are also obtained for homogeneous lossy elliptical cylinders and wedge-semicircle cross-sectioned cylinders, with and without a conducting cylinder in its center. RCS dependences on frequency and conductivity as well as the matrix stability problem of this surface integral equation method are also examined.     

Elliptic cylinder geometry for distinguishability analysis in impedance tomography

Electrical impedance tomography (EIT) is a technique that computes the cross-sectional impedance distribution within the body by using current and voltage measurements made on the body surface. It has been reported that the image reconstruction is distorted considerably when the boundary shape is considered to be more elliptical than circular as a more realistic shape for the measurement boundary. This paper describes an alternative framework for determining the distinguishability region with a finite measurement precision for different conductivity distributions in a body modeled by elliptic cylinder geometry. The distinguishable regions are compared in terms of modeling error for predefined inhomogeneities with elliptical and circular approaches for a noncircular measurement boundary at the body surface. Since most objects investigated by EIT are noncircular in shape, the analytical solution for the forward problem for the elliptical cross section approach is shown to be useful in order to reach a better assessment of the distinguishability region defined in a noncircular boundary. This paper is concentrated on centered elliptic inhomogeneity in the elliptical boundary and an analytic solution for this type of forward problem. The distinguishability performance of elliptical cross section with cosine injected current patterns is examined for different parameters of elliptical geometry.     

Losses in the PEMC Boundary

Perfect electromagnetic conductor (PEMC) was recently introduced to generalize both the perfect electric conductor (PEC) and the perfect magnetic conductor (PMC), which are used as boundary material. In this paper, an extension of PEMC boundary conditions is made to a more realistic model with small losses (“good electromagnetic conductor”). It is shown that the antisymmetric boundary impedance dyadic defining the ideal PEMC boundary cannot alone carry any losses and a symmetric component must be added that actually dominates the lossy behavior of the boundary. As an example, a slab of low-loss gyrotropic wave-guiding material is studied and shown to represent the lossy counterpart of the PEMC boundary. The effect of losses is demonstrated by considering plane-wave reflection from an imperfect PEMC plane.     

Theoretical evaluation of nonlinear tapers for a high-powergyrotron

The theoretical performance of two nonlinear circular waveguide tapers constructed for a 10-GHz, 30-MW amplifier utilizing the lowest circular electric mode is evaluated. Mode coupling is estimated with a code that solves the generalized telegraphist's equations numerically and is compared with the results of a cascaded scattering matrix code. It is found that assuming a sufficiently lossy conducting boundary allows evaluation of modes that pass through cutoff and that consideration of backward modes usually results in small changes in the forward modes that reconcile the two numerical procedures. A comparison of the raised cosine profile with other taper shapes is made. It is shown that, under some conditions, a raised cosine profile yields less mode conversion than the modified Dolph-Chebyshev profile     

High frequency loss and electromagnetic field distribution forstriplines and microstrips [MCM packages]

A new three-component measured equation of invariance (MEI) boundary condition is developed and applied to the hybrid edge/nodal vector finite element method. The electric field distribution on the cross section of various lossy transmission lines is calculated. The propagation constant of a lossy transmission line with coated conductor strip is also calculated. The three-component MEI boundary condition simulates the field distribution on the artificial boundary for electromagnetic field excited by the surface charge density and the three vector components of the electric current density. Numerical experiments are performed to test the method by comparing calculated transmission loss with the measured data     

Tunability limitations of microwave resonators tuned by several capacitances and inductances

Tunability limitations of resonators that consist of transmission line sections and are tuned by several capacitances and inductances are established. The limitations are common for lossy and lossless resonators. It is shown that an increase in the number of tuning elements does not lead to increasing frequency ratio. It is proved that combined tuning is more effective that tuning by one-type elements. This tuning makes possible continuous variation of the resonance frequency in a wide range exceeding a decade.     

Field Solution for Radial Waveguides with Annular Discontinuities

A method is established which gives the internal field of a radial waveguide in the presence of annular-type slots on the conducting walls or metallic scatterers inside the guide. The exciting field can have a general form, and the dielectric constant of the region could be lossy or lossless. To obtain a solution, the induced currents (magnetic current in case of slot-type discontinuity) over the scattering bodies are expanded into a finite series of suitable basis functions with unknown coefficients. The total number of these functions is directly related to the electrical dimensions of the scatterers. The complex coefficients are then obtained by employing the appropriate Green's functions and an application of the boundary conditions over the scattering bodies. The method is then applied to the probIem of coupling between two radials waveguides by annular slots on the common boundary. It is shown that in general, higher order modes have significant effect on the solution, and for a precise evaluation of the field their contribution must also be included.     

RCS analysis of canonical,two-dimensional material-loaded cavities with rectangular and circular cross sections

A rigorous radar cross section (rcs) analysis of canonical, two-dimensional material-loaded cavities with rectangular and circular cross sections is carried out using the Wiener-Hopf technique and the Riemann-Hilbert problem technique, respectively. Both E and H polarizations are treated. It is shown via numerical examples that the absorbing layer loading inside the cavities gives rise to the significant rcs reduction. The results can be used as a reference solution for validating more general-purpose computer codes based on approximate methods.     

Parallel-planes approximation for propagation in rectangular tunnels

Natural propagation of electromagnetic waves in rectangular tunnels is analysed using parallel lossy planes approximations with no restrictions on the electrical properties of the walls. The analysis provides a better understanding of the physical characteristics of the low-order modes as a function of frequency. Numerical results are compared satisfactorily with published measurements.     

Low-Frequency Behavior of the Propagation Constant Along a Thin Wire in an Arbitrarily Shaped Mine Tunnel

Seidel and Wait have investigated the complex propagation constant (phase and attenuation coefficients) of the fundamental mode of propagation for radio waves along a thin wire or cable, located in an elliptical mine tunnel, and found that the attenuation rate for low frequency is insensitive to the shape of the ellipse if the cable-wall distance and cross-sectional area are kept constant. We consider here tunnels of more general cross section, and obtain a characteristic equation for the propagation constant valid for sufficiently low frequency, by means of a variational formulation of an integral equation. The characteristic equation involves only the electrical parameter of the tunnel walls, the radius of the wire, and the capacitance per unit length that the wire would have if the tunnel walls were perfectly conducting. Agreement with exact calculations for several geometries is found to be excellent below about 100 kHz, and acceptable even up to 1 MHz or more, for typical tunnel parameters. Since the wire capacitance can be shown to depend most importantly on its distance from the wall and on the area of the tunnel, the conclusion of Seidel and Wait can be made more precise and extended to tunnels of arbitrary cross section.     

Performance of an array of circular waveguides with strip-loadeddielectric hard walls

An infinite planar periodic antenna array of radiating open-ended circular waveguides is considered. The conducting waveguide walls are covered with dielectric layers loaded with longitudinal conducting strips for providing the hard wall boundary condition. Analysis of the array is carried out by the mode-matching method. The waveguide modes involved in the method are calculated by using the asymptotic strip boundary condition. It is shown that they are split into an independent subsystem of TE modes for the whole cross section and two independent subsystems of TM modes: one is for the central region and another is for the layer region. The calculations show that the operation of the hard waveguides in an array with small element spacing is similar to that of the multimode smooth wall waveguides completely filled with dielectric. For large diameters and element spacing, the hard waveguides have significant advantages over the smooth ones. It is shown that unlike an individual hard waveguide, the aperture efficiency of such a waveguide in the array has a nonmonotonic dependence on the waveguide radius. The results characterizing the behavior of the aperture efficiency and cross-polarization level in a frequency band as well as the contribution of certain waveguide modes in the reflected power are presented and discussed. The examples of the element patterns corresponding to minimal cross polarization are also given     

A note on the radiation boundary conditions for the Helmholtzequation

The radiation boundary conditions in two dimensions are derived in the body-fitted coordinate system using the method of successive approximations for the wave envelope function. Results are valid for a convex scatterer with continuous radius of curvature on the surface of the scatterer. In the special case when the computational boundary is circular, the boundary operators derived are identical to the Bayliss operators. The on-surface radiation condition is examined. It is shown that, for a large conducting circular cylinder, a boundary operator of infinite order should be used due to the breakdown of the asymptotic expansions of the boundary operators on the surface of the scatterer. The leading order result based on the boundary operator of infinite order applied on the surface of the cylinder is the same as the result obtained by the method of physical optics     

Finite element formulation for lossy waveguides

An efficient computer-aided solution procedure based on the finite-element method is developed for solving general waveguiding structures composed of lossy materials. In this procedure, a formulation in terms of the transverse magnetic-field components is adopted and the eigenvalue of the final matrix equation corresponds to the propagation constant itself. Thus, it is possible to avoid the unnecessary iteration using complex frequencies. To demonstrate the strength of the presented method, numerical results for a rectangular waveguide filled with lossy dielectric are presented and compared with exact solutions. As more advanced applications of the presented method, a shielded image line composed of a lossy anisotropic material and a lossy dielectric-loaded waveguide with impedance walls are analyzed and evaluated     

Lossy Transmission Line Filters

Reactive bandpass and low-pass filters often exhibit spurious responses in the frequency region above the design passband. The spurious responses limit the effectiveness of the filter in preventing interference by out-of-band signals. A simple and inexpensive technique for reducing or eliminating these passbands is to add short sections of an appropriate lossy transmission line in series with the conventional filter. A significant size reduction of conventional transmission line reactive filters can also be realized along with the reduction or elimination of spurious passbands by combining a lossy dielectric with the conventional reactive elements. This paper discusses the application of lossy line filters in cascade with and integrated into conventional reactive filters. The design of lossy transmission line sections and wide-band impedance matching techniques are described.     

Transients on lossy transmission lines with arbitrary boundary conditions

In this work the problem of transients on a lossy transmission line terminated by an arbitrary, including nonlinear, load is formulated. The tranmission line parameters are the constantsR, L, G, andC. The exact relation between the input and output voltages and currents in the form of two coupled integral equations is derived by the Laplace transform method. It is shown that the kernels of the integral equations may be represented in terms of either Lommel functions or integrals involving zeroth order modified Bessel functions. Simultaneous (numerical) solutions of these integral equations fulfilling the boundary conditions at the input and output of the line yields the input and output voltages and currents on the line. Finally the exact analytical relations in time domain of the voltage and current at an arbitrary point on the line (and the voltages and currents at the input and output terminals) are derived. In all parts, the problem has been formulated in such a way as to impose the causality condition explicitly.     

Transient analysis of lossy parabolic transmission lines withnonlinear loads

The exact analytical expressions of the time-domain step response matrix parameters for the lossy parabolic transmission line are developed, therefore extending the range of problems where Allen's method can be applied for the transient analysis of networks consisting of interconnections of linear distributed elements, lumped linear and/or nonlinear elements, and arbitrary sources. For completeness, similar expressions are derived for the lossless parabolic line. In order to demonstrate the versatility of the techniques presented in this paper, we study the transient response of a lossy parabolic line subjected to the following sets of boundary conditions: 1) a unit step input and a linear load, and 2) a trapezoidal pulse generator and a nonlinear load