Numerically derived absorbing boundary condition for the solutionof open region scattering problems

An absorbing boundary condition is developed by means of a numerical approximation of the analytical behavior of the exact boundary condition. The boundary operator is more accurate than other analytically derived differential operators having the same order, and it can be applied to arbitrarily shaped scatterer geometries that can be handled most efficiently through the use of outer boundaries that conform to the body of the scatterer. Examples demonstrate the improvement in accuracy and efficiency achieved by the numerical boundary condition. The enhancement in accuracy is attributable to the inclusion of the evanescent harmonics behavior in the model     

数值吸收边界条件在OSRC方法中的应用

本文引入一种数值吸收边界条件,将其应用于解决开放空间电磁散射问题的表面辐射条件法(OSRC)之中。本文使用这种边界条件对理想导电及均匀电磁可穿透材料圆柱散射体的表面场进行了数值计算,并与使用二阶微分算子B_2型的吸收边界条件的结果作了比较。所有结果说明,这种数值吸收边界条件特大大改善OSRC方法的精度。     

Backscatter RCS for TE and TM excitations of dielectric-filledcavity-backed apertures in two-dimensional bodies

Transverse electric (TE) and transverse magnetic (TM) scattering from dielectric-filled, cavity-backed apertures in two-dimensional bodies are treated using the method of moments technique to solve a set of combined-field integral equations for the equivalent induced electric and magnetic currents on the exterior of the scattering body and on the associated aperture. Results are presented for the backscatter radar cross section (RCS) versus the electrical size of the scatterer for two different dielectric-filled cavity-backed geometries. The first geometry is a circular cylinder of infinite length which has an infinite length slot aperture along one side. The cavity inside the cylinder is dielectric filled and is also of circular cross section. The two cylinders (external and internal) are of different radii and their respective longitudinal axes are parallel but not collocated. The second is a square cylinder of infinite length which has an infinite length slot aperture along one side. The cavity inside the square cylinder is dielectric-filled and is also of square cross section     

The near field of a wire grid model

The extreme near-field behavior of the wire grid model of a conducting surface is examined. Using a wire grid model of an infinite transverse magnetic circular cylinder, it is verified that the best accuracy for the E-field is obtained when the wire satisfies the `same surface area' rule of thumb. Two excitations are considered: a uniform surface current and plane wave incidence. In the first case, although the boundary value match between the wires is poor the extreme near field is still quite accurate. In the second case, the near field is also accurate, however, the largest errors occur not between the wires, but in the interior of the scatterer. In both cases, the boundary match between the wires as a check on the accuracy of the solution is misleading     

EM Programmer's Notebook [EM scattering]

An interactive circular-cylinder modeler software program in which the approximation of a complex scatterer is achieved by using circular cylinders is described. The cylinders are made of either homogeneous isotropic dielectric material, perfectly conducting material characterized by a surface impedance, or a combination of the two. The user interface is designed for quick construction of two-dimensional scatterers using circular cylinders of arbitrary radii. The algorithm for multiple scattering between these cylinders is based on the enforcement of the appropriate boundary conditions on the surface of each cylinder. The source of excitation can be a plane wave or a line source parallel to the scatterer, and both TM and TE types of polarization are considered     

A finite element approach to the electromagnetic interaction withrotating penetrable cylinders of arbitrary cross section

A method for evaluating the fields excited by an obliquely incident plane wave inside and outside a rotating cylinder is presented. A differential formulation of the problem is developed with respect to the comoving reference frame of the scatterer on a closed circular domain including the scatterer cross section; the boundary conditions account for the far-field conditions through a series expansion of the total field on the domain contour. The results at oblique incidence are then particularized for normal incidence and a hybrid finite element numerical solution is presented and discussed for TM incidence. The present FEM approach and the related computer code are directly applicable to the study of rotating piecewise-homogeneous cylinders at normal incidence, as well as metallic cylinders coated by layers of penetrable materials. Through a comparison, for normal incidence, between the quasi-stationary and the Galileian relativistic approach, a method for approximately reconstructing the Doppler frequency shift in the quasi-stationary method is derived. Far-field and near-field numerical results for circular and arbitrarily shaped (metallic or dielectric) cylinders are presented     

FINITE DIFFERENCE METHOD FOR ELECTROMAGNETIC SCATTERING FROM PERFECTLY CONDUCTING CYLINDER

A numerical method of solving electromagnetic wave scattering problem is described.Radiation boundary condition(RBC)is applied to confine EM scattering problem in unboundedregion into problem in finite region.Combined with RBC and scatterer surface boundary condi-tion,Helmholtz equation in the finite region is solved numerically by the finite difference method.Thus the distribution of induced surface current on conducting cylinder and near field can beobtained.Computational results for both polarizations for circular,elliptic and square cylindersare presented.These results are in excellent agreement with those obtained by the eigenfunctionexpansion method or moment method and much better then the results of OSRC method.     

A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach

A new formulation of electromagnetic wave scattering by convex, two-dimensional conducting bodies is reported. This formulation, called the on-surface radiation condition (OSRC) approach, is based upon an expansion of the radiation condition applied directly on the surface of a scatterer. Past approaches involved applying a radiation condition at some distance from the scatterer in order to achieve a nearly reflection-free truncation of a finite-difference time-domain lattice. However, it is now shown that application of a suitable radiation condition directly on the surface of a convex conducting scatterer can lead to substantial simplification of the frequency-domain integral equation for the scattered field, which is reduced to just a line integral. For the transverse magnetic (TM) case, the integrand is known explicitly. For the transverse electric (TE) case, the integrand can be easily constructed by solving an ordinary differential equation around the scatterer surface contour. Examples are provided which show that OSRC yields computed near and far fields which approach the exact results for canonical shapes such as the circular cylinder, square cylinder, and strip. Electrical sizes for the examples areka = 5andka = 10. The new OSRC formulation of scattering may present a useful alternative to present integral equation and uniform high-frequency approaches for convex cylinders larger thanka = 1. Structures with edges or corners can also be analyzed, although more work is needed to incorporate the physics of singular currents at these discontinuities. Convex dielectric structures can also be treated using OSRC. These will be the subject of a forthcoming paper.     

On the applicability of OSRC method to homogeneous scatterers

The author investigates the application of radiation boundary conditions to two-dimensional scattering by a homogeneous penetrable cylinder. The second-order radiation boundary operator proposed by G.A. Kriegsmann et al. (1987) is applied on a conformal outer boundary enclosing the object. By taking the specific case of a lossless circular cylinder for which the exact solution exists it is shown that the on-surface radiation condition (OSRC) method does not necessarily yield accurate results for all values of material constants. Highly erroneous results are produced for certain values of permittivity and permeability, while acceptable results can be obtained for others. The author suggests that the cause of these erroneous results is related directly to the error in the reactive portion of the complex scattered power. However, as the outer boundary of the radiation condition recedes away from the object contour, the error is shown to diminish. Numerical results are presented for the bistatic echo width for both transverse electric (TE) and transverse magnetic (TM) polarizations     

Electromagnetic wave scattering from some vegetation samples

For an incident plane wave, the field inside a thin scatterer (disk and needle) is estimated by the generalized Rayleigh-Gans (GRG) approximation. This leads to a scattering amplitude tensor equal to that obtained via the Rayleigh approximation (dipole term) with a modifying function. For a finite-length cylinder the inner field is estimated by the corresponding field for the same cylinder of infinite length. The effects of different approaches in estimating the field inside the scatterer on the backscattering cross section are illustrated numerically for a circular disk, a needle and a finite-length cylinder as a function of the wave number and the incidence angle. Finally, the modeling predictions are compared with measurements     

An iterative method for solving scattering problems

An iterative method is developed for computing the current induced by plane wave excitation on conducting bodies of arbitrary shape. In this method, the scattering body is divided into lit- and shadow-side regions separated by the geometric optics boundary. The induced current at any point on the surface of the scatterer is expressed as the sum of an approximate optics current and a correction current. Both of these currents are computed by iteration for the lit and shadow regions separately. The general theory is presented and applied to the problems of scattering from a two-dimensional cylinder of circular and square cross sections. The results are compared with the method of moments and good agreement is obtained. This method does not give erroneous results at internal resonances of the scatterer, does not suffer from computer storage problems and can be extended to nonperfect conductors as well as to three-dimensional bodies.     

About the choice of auxiliary sources during the solution of the problem of diffraction of a point source field by a dielectric body

A new version of the modified method of discrete sources (MMDSs) is proposed for the solution of the 2D and 3D (vector) problems of diffraction of the point source field by a dielectric body. The case when the source is located at a small distance from a scatterer is considered. The method is tested for the example of the problem of diffraction of a point source field by an infinite dielectric cylinder and a dielectric sphere. It is shown that the discrepancy of the boundary conditions is substantially lower when the suggested variant of the MMDSs is used for various geometries of a scatterer.     

Radiation characteristics of corrugation loaded dielectric-coated conducting cylinder

The radiation characteristics of a corrugation loaded dielectric coated conducting cylinder are investigated theoretically for the infinite periodic and finite structures. For the infinite periodic structure, the mode matching method is applied. The integral equation is derived for the finite structure by use of the Fourier transform and mode expansion. The influences of the corrugation width, corrugation depth, dielectric thickness, cylinder radius, and finite corrugation number on the radiation characteristics (leakage constant, phase constant, and radiation pattern) are investigated. The results of the finite periodic corrugations are compared with those of the infinite extent structure and good agreement is found. To reduce the high side lobe of the uniform periodic structure, nonuniform quasiperiodic corrugation arrays are considered. The surface wave radiated by the structure having end-fire radiation pattern is also investigated.     

Radar cross-section study of cylindrical cavity-backed apertureswith outer or inner material coating: the case of H-polarization

A dual-series-based solution is obtained for the scattering of an H-polarized plane wave from a slitted infinite circular cylinder coated with absorbing material from inside or outside. For both cases, numerical results are presented for the radar cross section and comparisons are given for two different realistic absorbing materials. The radar cross-section dependencies are also given for the aspect angle of the scatterer and the thickness of the absorbing layer     

Numerical analysis and validation of the combined field surfaceintegral equations for electromagnetic scattering by arbitrary shapedtwo-dimensional anisotropic objects

The numerical solution of coupled integral equations for arbitrarily shaped two-dimensional, homogeneous anisotropic scatterers is presented. The combined theoretical and numerical approach utilized in the solution of the integral equations is based on the combined field formulation and is specialized to both transverse electric (TE) and transverse magnetic (TM) polarizations. As opposed to the currently available methods for anisotropic scatterers, the present approach involves integration over the surface of the scatterer in order to determine the unknown surface electric and magnetic current distributions. The solution is facilitated by developing a numerical approach employing the method of moments. The various difficulties involved in the numerical effort are pointed out, and ways of overcoming them are discussed in detail. The results obtained for two canonical anisotropic structures, namely, a circular cylinder and a square cylinder, are given and validated by results obtained by alternative methods     

Electromagnetic scattering from an eccentric multilayered circularcylinder

Electromagnetic scattering from an eccentric multilayered, homogeneous, circular cylinder is derived rigorously by using a boundary value mode-matching approach. The layers are assumed to be infinite in length and their axes are parallel to each other but their centers may have arbitrary coordinates. The composite arrangement is illuminated by a cylindrical wave from a line source of infinite extent in a direction parallel to the cylinder axis. The problem is two-dimensional and the solution to both types of polarization is presented. The effects of various geometrical and electrical parameters on the near- and far-field patterns are examined     

Impedance boundary conditions in ultrasonics

A generalized impedance boundary condition (GIBC) is developed to approximate the scattering of a plane acoustic wave from a bone structure such as a rib. In particular, the rib and surrounding tissue are modeled as a viscoelastic cylinder of infinite length immersed in an infinite, inviscid fluid medium. In order to determine the scattered pressure wave, appropriate boundary conditions are imposed on the relevant differential equations at the fluid-solid surface. The exact solution is then used to develop first- and second-order impedance boundary conditions applicable at the surface of the cylinder. Numerical results demonstrate the improved accuracy of the second order condition     

Electromagnetic scattering from a dielectric coated cylinder using OSRC-GMT

The electromagnetic scattering from a dielectric coated cylinder is analysed based on the generalised multipole technique (GMT) combined with the on-surface radiation condition (OSRC) for separating an open region of inhomogeneous media into the inside region of the homogeneous medium and the outside region of free space. The equivalent multipole sources inside which produce the outside scattered fields, are determined by the OSRC on the outer surface. Some numerical examples for calculating the RCS from the scatterer with concentrically circular or confocally elliptic cross-section are provided.<>     

A boundary-element solution of the Leontovitch problem

A boundary-element method is introduced for solving electromagnetic scattering problems in the frequency domain relative to an impedance boundary condition (IBC) on an obstacle of arbitrary shape. The formulation is based on the field approach; namely, it is obtained by enforcing the total electromagnetic field, expressed by means of the incident field and the equivalent electric and magnetic currents and charges on the scatterer surface, to satisfy the boundary condition. As a result, this formulation is well-posed at any frequency for an absorbing scatterer. Both of the equivalent currents are discretized by a boundary-element method over a triangular mesh of the surface scatterer. The magnetic currents are then eliminated at the element level during the assembly process. The final linear system to be solved keeps all of the desirable properties provided by the application of this method to the usual perfectly conducting scatterer; that is, its unknowns are the fluxes of the electric currents across the edges of the mesh and its coefficient matrix is symmetric     

Wire grid modeling of surfaces

When a surface is numerically modeled with a wire grid, results are sensitive to the wire diameter. It is shown that the best accuracy is obtained when the wire satisfies the "same surface area" rule of thumb, for the canonical problem of scattering (or radiation) from an infinite circular cylinder. It is important to note that wires that are too thick are just as bad as wires that are too thin. It is also shown that the boundary value match between wires is not a reliable check on the validity of farfield results. Finally, data are given on the effect of wire spacing. Results are obtained from exact solutions of both the true problem and the wire grid model, thus isolating the effects of wire grid modeling per se.