Ning Yan Zhu

Modeling radio wave propagation in tunnels with a vectorial parabolic equation

To study radio wave propagation in tunnels, we present a vectorial parabolic equation (PE) taking into account the cross-section shape, wall impedances, slowly varying curvature, and torsion of the tunnel axis. For rectangular cross section, two polarizations are decoupled and two families of adiabatic modes can be found explicitly, giving a generalization of the known results for a uniform tunnel. In the general case, a boundary value problem arises to be solved by using finite-difference/finite-element (FD/FE) techniques. Numerical examples demonstrate the computational efficiency of the proposed method.

Exact solution to diffraction problem by wedges with a class of anisotropic impedance faces: oblique incidence of a plane electromagnetic wave

This paper studies diffraction of an obliquely incident, arbitrarily polarized plane electromagnetic wave by an anisotropic impedance wedge with an opening angle 2/spl Phi/ between 0 and 2/spl pi/, and presents a closed-form exact solution to a class of impedance wedge faces and the related uniform asymptotic solution (UAS). On use of a unitary similarity transform, the boundary conditions on the wedge faces is brought into a form, which makes the exactly soluble class of impedance faces evident. The exact solution is found with help of the Sommerfeld-Malyuzhinets (1896, 1958) technique, a generalized Malyuzhinets function /spl chi//sub /spl Phi// and the so-called S-integrals. A standard procedure yields therefrom the UAS. The exact solution agrees with known analytical results in special cases, and the numerical results of UAS are confirmed by that of parabolic equation method (PEM).

Analytical-Numerical Calculation of Diffraction Coefficients for a Circular Impedance Cone

An analytical-numerical computation of diffraction coefficients is described for a semi-infinite impedance cone of circular cross section illuminated by an electromagnetic plane wave. To enable an incomplete separation of variables, both the incident and scattered fields are expressed in terms of the Kontorovich-Lebedev (KL) integrals; an inversion of the Leontovich condition on the cones surface yields equations for the spectra, whose Fourier coefficients satisfy certain functional difference equations of the second order; the latter are then converted to integral equations of the second kind which are solved numerically; using the so obtained spectra in the KL-integrals for the scattered field and evaluating the integrals in far field leads to diffraction coefficients. Numerical results are included both for verification purposes and for displaying the diffraction behavior for different incident and diffraction angles, as well as for several cone impedances.

A solution procedure for second-order difference equations and its application to electromagnetic-wave diffraction in a wedge-shaped region

This paper proposes an efficient solution procedure for second–order functional difference equations, and outlines this procedure through investigating electromagnetic–wave diffraction by a canonical structure comprising an impedance wedge and an impedance sheet bisecting the exterior region of the wedge. Applying the Sommerfeld–Malyuzhinets technique to the original boundary–value problem yields a linear system of equations for the two coupled spectral functions. Eliminating one spectral function leads to a second-order difference equation for the other. The chief steps in this work consist of transforming the second–order equation into a simpler one by making use of a generalized Malyuzhinets function χφ(α), and in expressing the solution to the latter in an integral form with help of the so–called S–integrals. From this integral expression one immediately obtains a Fredholm equation of the second kind for points on the imaginary axis of the complex plane. Solving this integral equation by means of the well–known quadrature method enables us to calculate the sought–for spectral function inside the basic strip via an interpolation formula and outside it via an analytic extension. The second spectral function is obtained through its dependence upon the first. The uniform asymptotic solution, which is of particular interest in the geometrical theory of diffraction, follows, by evaluating the Sommerfeld integrals in the far field from the exact one. Several examples demonstrate the efficiency and accuracy of the proposed procedure as well as typical behaviour of the far–field solutions for such a canonical problem of diffraction theory.

Application of curved parametric triangular and quadrilateral edge elements in the moment method solution of the EFIE

The authors report the application of curved parametric triangular and quadrilateral edge elements as basis functions in the moment method (MM) solution of the electric field integral equation (EFIE). In this way, an arbitrarily shaped surface can be modeled more accurately than with conventional planar patches. Consequently, higher accuracy in the numerical solution can be obtained, as demonstrated by numerical examples.<<ETX>>

Diffraction of a normally incident plane wave at a wedge with identical tensor impedance faces

Diffraction of a normally incident plane wave by a wedge with identical tensor impedance faces is studied and an exact solution is obtained by reducing the original problem to two decoupled and already solved ones. A uniform asymptotic solution then follows from the exact one and agrees excellently with numerical results due to the method of parabolic equation.

Diffraction of a normally incident plane wave by an impedance wedge with its exterior bisected by a semi-infinite impedance sheet

This paper reports an application of a previously proposed procedure to diffraction of a normally incident, arbitrarily polarized plane electromagnetic wave by a canonical structure which consists of a wedge with different face impedances and a semi-infinite impedance sheet bisecting the exterior of the wedge. The use of the Sommerfeld-Malyuzhinets technique converts the original boundary value problem into a system of linear equations for two coupled spectral functions. Eliminating one of them, we get a second-order difference equation for the other spectral function. From this function and the boundary condition on the upper wedge face we construct an even and in the basic strip regular new spectral function. Then we transform the second-order equation into a simpler one by means of a generalized Malyuzhinets function /spl chi//sub /spl Phi//(/spl alpha/), and express the solution to the latter in an integral form with help of the so-called S-integrals. Solving a Fredholm equation of the second kind for points on the imaginary axis of the complex plane, which follows from the integral representation, enables one to compute the sought-for function. The second spectral function is obtained via its dependence upon the first one. We present a first-order uniform asymptotic solution, as well as numerical results.

Numerical Modelling of Pulse Propagation in Tunnels

Recently, a vectorial parabolic equation has been derived for modelling the propagation of time-harmonic electromagnetic waves in tunnels. This paper reports an extension of this paraxial approximation to transient phenomena, namely a time-domain vectorial parabolic wave equation, obtained by analytically Fourier-transforming its frequency-domain counterpart. An efficient and absolute stable solution procedure for the vectorial, four-dimensional approximate wave equation is presented and examples of pulse propagation in tunnels are given. Index Terms – Numerical modelling, paraxial approximation, pulse propagation, tunnel

Electromagnetic Scattering of a Dipole-Field by an Impedance Wedge, Part I: Far-Field Space Waves

This paper consists of two parts and deals with the scattering of the wave-field generated by a Hertzian dipole placed over an impedance wedge. Expanding the dipole field into plane waves and extending to complex “angles of incidence” our recently obtained exact solution of the diffraction of a skew-incident plane wave by an impedance wedge enables us to give an integral representation for the total field. Then by means of asymptotic evaluation of the multiple integral far-field expressions are developed and interpreted. In the present first part (I) of the paper formulation and basic steps of analysis are presented. In particular, the far-field expressions for the reflected and edge waves, including the UAT (uniform asymptotic theory of diffraction) version of the far-field representation, are given. Both numerical computation and physical explanation of the analytic results have been performed. The forthcoming second part (II) of the work will be dedicated to the study of different surface waves excited, as well as to their physical interpretation and numerical calculation.

An efficient FEM formulation for rotationally symmetric coaxial waveguides

In this paper, an efficient finite element method formulation (FEM) is applied to rotationally symmetric coaxial waveguides, in which the dependence of the dominant TEM mode on the radius of the cylindrical coordinate system is explicitly taken into account in the basis functions. In this way, a physically appropriate approximation of the unknown field distribution is achieved. After scaling, the resulting sparse matrix equation is solved iteratively by using the biconjugate gradient method (BCG). The numerical results show excellent agreement with results of the mode matching technique (MMT). Compared with the conventional FEM formulation, this method yields a significant improvement in accuracy within the frequency range where the TEM mode dominates. >