Matrix formulation of electromagnetic scattering

A new method is proposed for the computation of the radar cross section and other associated field quantities arising when a smooth, perfectly conducting obstacle is illuminated by an incident electromagnetic wave. The scattered wave is first represented by a distribution of electric dipoles over the surface in question, with the response from any dipole proportional to the induced surface current density at that point. The surface current is then determined by the "boundary condition" that the scattered wave, through interference, precisely cancels the incident wave inside the obstacle. One obtains in this mariner a pair of coupled (infinite) matrix equations for the surface current. Green's identity permits decoupling of the equations, reducing the problem to roughly the equivalent of two independent scalar problems. The equations have been specialized to axially symmetric obstacles and then solved numerically on the IBM 7094 for several examples of interest. Reciprocity and energy conservation are also examined and the resonant mode (interior) problem set up explicitly in matrix form.     

Multifrequency formulation for electromagnetic scattering usingshifted-frequency internal equivalence

A new formulation for multifrequency electromagnetic scattering problems involving homogeneous or inhomogeneous bodies is introduced and discussed. The formulation is developed using the shifted-frequency internal equivalence in the construction of the internal equivalence in the scattering problem. With this approach, the equivalent currents for the internally equivalent problem radiate a chosen fixed frequency which is different from the frequency of the incident wave. These equivalent currents are functions of the incident and shifted frequencies, material parameters, and the total field inside the body and on its boundary. A combination of this internally equivalent problem with an externally equivalent one, so as to match the tangential fields at the boundary of the body, results in the new formulation. The formulation and its application to generate multifrequency data using internal data generated at a single frequency in a volume-surface integral-equation approach utilizing the method of moments in the solution are explained and exemplified using a simple inhomogeneous slab problem     

A state-space formulation of transient electromagnetic scattering

For a perfectly conducting scatterer, a state-space formulation for the transient scattered field is given for single-input and multiple-output. The formulation is based on the meromorphic property of the scattered field and includes the constraint that the natural body resonances are invariant with observation point.     

An open surface integral formulation for electromagnetic scattering by material plates

Using the surface equivalence theorem, four coupled integral equations are developed for electromagnetic scattering by a thin material plate. Using symmetry properties, it is shown that these equations can be written as open surface integral equations. Surface impedance relationships are obtained and used to eliminate two of the four integral equations. The remaining two equations are solved using the method of moments (MM). Numerical results for penetrable and impenetrable material plates are in reasonable agreement with measurements.     

The null field approach to electromagnetic scattering fromcomposite objects

An improved null-field approach to scattering from composite objects is reported. Several alternative expressions for the transition matrix of a composite object are derived that partly or completely avoid the geometrical constraints inherent in previous null-field results for a composite scatterer. Some of the new versions make use of Q-matrices for the open surfaces which are defined by the interfaces between the different parts of the composite scatterer. The numerical performance of the various alternatives is investigated for a number of test cases. Comparisons between alternative versions for the same scattering problem are made to provide a measure of the absolute accuracy of the computed null-field results. Whenever possible, the results are compared with other computed or measured results     

多层圆柱形磁性体的散射场

以改善法向模螺旋天线的特性为目的，对平面波入射时任意媒质常数为参量的多层圆柱形磁性体的散射反射电磁场特性及内部磁通进行了研究和解析，数值计算的结果中作为改善法向模螺旋天线性能抑制反射、散射现象的指导性设计资料。     

The application of contraction theory to an iterative formulation of electromagnetic scattering

Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (ork-space) formulation is presented with an emphasis on application to periodic surfaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.     

The tolerance method for electromagnetic scattering

The original electromagnetic field will be disturbed when the parameter of a local region is changed. To find the distribution of the disturbed electromagnetic field a boundary value problem, which is different from the original one, must be solved. A method to find the disturbed electromagnetic field from the known original one with a minimum amount of computation would be very significant. In this paper, we present a method, tolerance method, which can save significant computer time in the computation of the disturbed electromagnetic field. This method can be used for many complicated boundary value problems as well as for optimum design in engineering. An example of the computation of an electromagnetic scattering problem is given in this paper     

Combined field integral equation formulations for electromagnetic scattering from convex geometries

The properties of different forms of the combined field integral equation (CFIE) formulation of electromagnetic scattering from convex, perfect electrically conducting geometries are considered. Several difficulties encountered in the numerical implementation of the traditional CFIEs of electromagnetic scattering theory are discussed. An alternate form of the CFIE is introduced which is free of many of the deficiencies of traditional formulations for smooth, convex geometries. The improved numerical properties of the new formulation are illustrated with numerical examples.     

The bymoment method for two-dimensional electromagnetic scattering

The bymoment method is presented for analyzing two-dimensional electromagnetic wave scattering in an unbounded region. The method introduces a conforming surface to geometrically decouple the interior region containing the scatterer from the exterior region extending to infinity. The solution in the interior is generated using the standard finite-element solution of an interior Dirichlet boundary-value problem. The interior solution is then coupled to the exterior using Green's theorem in the unbounded exterior region. The validity of the method and the associated computer program is demonstrated by comparing the results to those of other methods for scattering by various cylindrical geometries     

The biconjugate gradient method for electromagnetic scattering

The biconjugate gradient (BCG) method for solving linear systems is shown to be more efficient than the conjugate gradient (CG) method for several examples from electromagnetic scattering. A remedy for the occasional stagnation of the algorithm is proposed. The potential flaw in the BCG algorithm may be avoided when encountered by restarting the algorithm with a perturbed estimate of the solution     

Combined field integral equation formulation for scattering by dielectrically coated conducting bodies

The combined field integral equation (CFIE) formulation for electromagnetic scattering from perfectly conducting bodies is generalized to treat conductors with layered dielectric coatings. The generalized formulation is proved to provide unique solutions at all frequencies. The method of moments is used to solve the resulting system of integral equations. Solutions in terms of two integral operators are developed for body of revolution configurations. The behavior and properties of the generalized combined field formulation are illustrated with results of calculations for coated spheres, cylinders, and cones.     

The scattering matrix formulation for overmoded coaxial cavities

The scattering matrix formulation for complex right-circular activities is extended to coaxial circuits with variable inner radii. The modified eigenvectors, which include the TEM wave, and the modified boundary conditions are presented. The properties of several configurations are examined and transmission measurements are shown to be in good agreement with theory     

电磁场计算中的MLPG-FE耦合新方法

针对现有各种无网格与有限元耦合思路的利弊,提出一种新的无网格局部Petrov-Galerkin-有限元耦合(MLPG-FE)方法,应用其成功求解了电磁场问题.在有限元与无网格的过渡区域内,对T.Belytschko提出的传统斜坡函数进行改进,使得交界面上求解场变量及其导数的连续性同时得到了保证,且可精确实施第一类边界条件.电磁场数值算例给出了令人满意的结果.     

Field computations and network representations for open electromagnetic structures

Rigorous network representations for radiating structures are still an open problem. In this contribution the concept of Transition Region for deriving such a network representation of complex structures radiating into free-space is introduced. The space is divided into one or more computational domains which contain the complex geometrical features embedded into a transition region delimited by an outer spherical surface. The introduction of the transition region is expedient to avoid a large computational domain of spherical shape. A theoretical investigation of the computational procedures for deriving the transition region network representation is also presented.     

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.     

The electromagnetic inverse scattering problem for layered dispersionless dielectrics

The problem of exactly reconstructing the one-dimensional refractive index profile of a dispersionless dielectric from reflection data is considered. The available data consist of reflection coefficient measurements at many wavenumbers due to a normally incident electromagnetic plane wave upon a dielectric half-space or equivalently the impulse response measurement of the half-space. A closed-form analytical technique is described and applied to several solutions. These solutions are compared with results from a numerical method that uses leapfrogging in space and time and other analytical methods. Finally, the robustness of this technique with respect to imprecise and bandlimited data is examined and compared with a previous result.     

A FAFFA-MLFMA algorithm for electromagnetic scattering

Based on the multilevel fast multipole algorithm (MLFMA), an efficient method is proposed to accelerate the solution of the combined field integral equation in electromagnetic scattering and radiation, where the fast far-field approximation (FAFFA) is combined with MLFMA. The translation between groups in MLFMA is expensive because spherical Hankel functions and Legendre polynomials are involved and the translator is defined on an Eward sphere with many k/spl circ/ directions. When two groups are in the far-field region, however, the translation can be greatly simplified by FAFFA where only a single k/spl circ/ direction is involved in the translator. The condition for using FAFFA and the way to efficiently incorporate FAFFA with MLFMA are discussed. Complexity analysis illustrates that the computational cost in FAFFA-MLFMA can be asymptotically cut by half compared to the conventional MLFMA. Numerical results are given to verify the efficiency of the algorithm.     

The null field approach to electromagnetic scattering fromcomposite objects: the case of concavo-convex constituents

Time-harmonic electromagnetic scattering from a composite body consisting of a (dielectric or metallic) core plus one or several dielectric coatings was studied using the null-field approach. Previously developed null-field approaches to scattering from composite bodies do not apply when these coatings are of concavo-convex shapes. The authors examine this case and develop alternative null-field approaches to such geometries. While the scattering problem is usually solved by determination of the total transition matrix, referring to spherical waves, for the composite scatterer, the authors' approaches lead to different algebraic expressions for the transition matrix. Two main alternatives are studied. One of these makes use of Q-matrices for open surfaces while the other is based on a limit procedure applied to a previously developed formalism for layered scatterers. The numerical accuracy of the results is less than that obtained for homogeneous scatterers of similar exterior shape and electrical size. The convergence of the numerical implementation of the equations is studied in terms of several indicators such as dependence on the truncation order, the accuracy with which general constraints such as symmetry and unitarity are fulfilled, and the influence of different choices of expansion functions obtained from a moment-method solution     

The inverse electromagnetic scattering problem for a perfectly conducting cylinder

The problem of determining the shape of the cross section of a simply connected perfectly conducting infinite cylinder from a knowledge of the far-field pattern for all angles of observation and small values of the wavenumber is considered. The method proposed relies heavily on conformal mapping techniques. In particular it is shown that if the transfinite diameter is known each Fourier coefficient of the far-field pattern of the electric field determines a Laurent coefficient of the conformal mapping taking the exterior of the unit disk onto the exterior of the unknown cross section. The transfinite diameter is determined by changing the polarization of the incoming wave and measuring the far-field pattern of the resulting magnetic field. Of particular interest is the case when only a finite number of the Fourier coefficients of the far-field pattern are known. In this situation error estimates are obtained by using results on coefficient estimates for univalent functions.