Electromagnetic scattering by a curved plate--Solution by uniform asymptotic theory of diffraction

The uniform asymptotic theory (UAT) of diffraction has been applied to find the monostatic scattered field by curved plate with a plane wave illumination with electric field parallel to the edge. The solution is valid for all positions of the receiver and is uniform around the reflection boundaries. The theoretical monostatic radar cross section (RCS) shows good agreement with experimental results. The formulation works very well for arbitrary radius of curvature of the plate down to a value oflambda/2.     

A uniform asymptotic theory of electromagnetic diffraction by a curved wedge

Diffraction of an arbitrary electromagnetic optical field by a conducting curved wedge is considered. The diffracted field according to Keller's geometrical theory of diffraction (GTD) can be expressed in a particularly simple form by making use of rotations of the incident and reflected fields about the edge. In this manner only a single scalar diffraction coefficient is involved. Near to shadow boundaries where the GTD solution is not valid, a uniform theory based on the Ansatz of Lewis, Boersma, and Ahluwalia is described. The dominant terms, to the order ofk^{-1/2}included, are used to compute the field exactly on the shadow boundaries. In contrast with the uniform theory of Kouyoumjian and Pathak, some extra terms occur: one depends on the edge curvature and wedge angle; another on the angular rate of change of the incident or reflected field at the point of observation.     

Uniform asymptotic solution for the diffraction by a discontinuity in curvature

An asymptotic solution for the electromagnetic diffraction by a discontinuity in curvature in a perfectly conducting surface or in an impedance surface is developed. The solution is uniform through the reflection transition region. It is of the uat type and gives the field in the transition region up to the order k^-3/2 included where k is the wave number. It is continuous and all its derivatives in the direction normal to the transition direction are continuous. The solution is established for a curvature discontinuity along a generatrix of a two dimensional surface illuminated by a plane wave. Its efficiency is illustrated by numerical examples.     

Modified asymptotic solution for the 2-dimensional scattering by a conducting strip

The authors' modified diffraction coefficient, previously used to compute the higher-order edge-edge interaction terms in the 2-dimensional diffraction by narrow slits and circular apertures, is used to solve for the scattering by a narrow conducting strip. By comparison with the results of Keller, Yu and Rudduck, and the exact solution, it is shown that the coefficient may be used with confidence for evaluating the backscattering cross-section, echo width and diffraction pattern of the strip.     

A hybrid asymptotic solution for the scattering by a pair ofparallel perfectly conducting wedges

The overlapping transition regions of the double diffraction by a pair of parallel wedge edges are considered for the hybrid case where the gap between the edges is small compared to the distances from the source and the observation point (plane-wave-far-field limit) and the scatterer as a whole is large (or infinite). A closed-form asymptotic solution for the scattered field continuous at all angles of incidence and scattering is constructed for this case. The peculiar feature of this solution is a hybrid representation of the field singly diffracted by the first wedge: a part of it is described by a nonuniform, geometrical theory of diffraction (GTD) expression, while the other part is described in terms of the uniform theory of diffraction (UTD). The rest of the diffracted ray fields are described by nonuniform expressions, with singularities mutually canceling on summation. This solution is applied to the scattering by a perfectly conducting rectangular cylinder with appropriate geometrical parameters, and agreement with moment method calculation is demonstrated     

A uniform GTD analysis of the diffraction of electromagnetic waves by a smooth convex surface

The problem of the diffraction of an arbitrary ray optical electromagnetic field by a smooth perfectly conducting convex surface is investigated. A pure ray optical solution to this problem has been developed by Keller within the framework of his geometrical theory of diffraction (GTD). However, the original GTD solution fails in the transition region adjacent to the shadow boundary where the diffracted field plays a significant role. A uniform GTD solution is developed which remains valid within the shadow boundary transition region, and which reduces to the GTD solution outside this transition region where the latter solution is valid. The construction of this uniform solution is based on an asymptotic solution obtained previously for a simpler canonical problem. The present uniform GTD solution can be conveniently and efficiently applied to many practical problems. Numerical results based on this uniform GTD solution are shown to agree very well with experiments.     

An asymptotic solution for the diffraction by a discontinuity in curvature coupled with surface diffraction

An extension is developed for the asymptotic theory of electromagnetic diffraction by a discontinuity in curvature on a smooth convex perfectly-conducting surface. It covers the case where the rays incident on and diffracted from the discontinuity are nearly tangent to the surface or are creeping rays, so that surface diffraction is involved. This extension is restricted to those diffracted rays lying on the same side of the discontinuity as the incident ray; this includes backscatter but excludes forward scattering.     

The asymptotic solution of the diffraction problems of the efectromagnetic waves by a perfect comductor

In this paper, the two dimentional problems of the diffraction of the electromagnetic waves by a perfect conductor are discussed by using the perturbational mapping function in Savin’s form. The general method and asymptotic formulas to solve this problem are presented. Especially, for the asymptotic solutions based on a circular cylindrical conductor, the formulas to calculate “O”—order and “I”—order asymptotic solution are given     

Diffraction by a half-plane with two face impedances uniform asymptotic expansion for plane wave and arbitrary line source incidence

A uniform asymptotic expansion (UAE) of Maliuzhinets' exact solution for incident plane wave diffraction by a half-plane with two face impedances has been obtained using Van der Waerden's method. This solution has been further extended to the case of arbitrary line source incidence using a heuristic approach.     

On the solution of coupled system of PDE by a multigrid method

A multigrid method based on the domain partitioning approach is presented in this work. A special prolongation technique is used to provide accurate boundary conditions and good initial iterate for the reduced problems on partitioned domains. When used in a high-order τ-extrapolated multigrid setting, this technique provides highly accurate solution on the finest grid on the portion of the domain where the solution is smooth. The prolongation technique is also useful in obtaining good initial guesses on the finest grid for any Newton-like multigrid method.     

Transition functions for high-frequency diffraction by a curvedperfectly conducting wedge. II. A partially uniform solution for ageneral wedge angle

For pt.I see ibid., vol.37, no.9, p.1073-9(1989). In pt.I, transition function solutions for the combined surface-edge diffraction were derived from the rigorous, canonical solution for a thin cylindrically curved sheet. Here, similar solutions are derived for the more general case of diffraction by a perfectly conducting curved wedge. In the absence of a canonical solution for this case, the theory developed here is a physical one. It is an extension of the spectral theory of diffraction to the Fock solution for the penumbra region field near a convex surface. For certain domains of illumination aspects and field points, this procedure recovers the results obtained by other authors, starting, however, from more plausible assumptions and providing a ne insight. For other domains, it yields asymptotic solutions for the first time, thus demonstrating greater generality than in the previous approaches. The results are checked in two ways: first, they reduce to the rigorous results of pt.I when specialized to a curved sheet; second, they are shown to agree with a moment-method solution for a structure involving a curved wedge     

On a possibility of constructing a refined heuristic solution for the problem of diffraction by a plane angular sector

It is shown that analytical solution of the problem of diffraction of an electromagnetic wave by a plane angular sector can be refined by applying the modified heuristic equivalent edge current method (EECM). The concept of a virtual imaginary edge oriented at an angle to a real edge is introduced. With the use of this concept, a known 2D solution can be applied instead of integration over an elementary strip for modifying the EECM. The EECM solution is refined through heuristically taking into account the influence of the edge end on the scattered signal. Computation results demonstrating good coincidence with known data are presented.     

On the solution of a class of large body problems with partialcircular symmetry (multiple asymmetries) by using a hybrid-dimensionalfinite-difference time-domain (FDTD) method

This paper presents an efficient method to solve a large body scattering problem, viz. a paraboloid reflector antenna system, with only partial circular symmetry. The asymmetry in the system is introduced by two factors, viz. the microstrip feed and an inhomogeneous radome. The paper presents a novel approach, based on the equivalence and reciprocity principles and the “equivalent” aperture theory, to overcome the asymmetry problem. The technique thereby enables substantial computational efficiencies by analyzing the majority of the three-dimensional (3-D) computational domain in an effective two-dimensional (2-D) simulation, with the remainder being analyzed using a 3-D algorithm     

On the solution of a class of large body problems with full orpartial circular symmetry by using the finite-difference time-domain(FDTD) method

This paper presents an efficient method to accurately solve large body scattering problems with partial circular symmetry. The method effectively reduces the computational domain from three to two dimensions by using the reciprocity theorem. It does so by dividing the problem into two parts: a larger 3-D region with circular symmetry, and a smaller 2-D region without circular symmetry. An finite-difference time-domain (FDTD) algorithm is used to analyze the circularly symmetric 3-D case, while a method of moments (MoM) code is employed for the nonsymmetric part of the structure. The results of these simulations are combined via the reciprocity theorem to yield the radiation pattern of the composite system. The advantage of this method is that it achieves significant savings in computer storage and run time in performing an equivalent 2-D as opposed to a full 3-D FDTD simulation. In addition to enhancing computational efficiency, the FDTD algorithm used in this paper also features one improvement over conventional FDTD methods: a conformal approach for improved accuracy in modeling curved dielectric and conductive surfaces. The accuracy of the method is validated via a comparison of simulated and measured results