R. Gordon

Finite element analysis of axisymmetric radomes

A two-step technique for the analysis of axisymmetric radomes is presented. Initially, an axisymmetric finite-element approach is employed, together with an absorbing boundary condition for mesh truncation, to determine the near fields scattered by an empty radome illuminated by a distant source. Next, the reciprocity theorem is invoked to determine the far-field pattern of an antenna encased by the radome, by computing the interaction between the current distribution on the antenna and the near-field data determined in the first step. The details of the formulation are presented along with numerical results for two different arrays enclosed by radomes of varying permittivities. >

A review of absorbing boundary conditions for two and three-dimensional electromagnetic scattering problems

The derivation of two- and three-dimensional absorbing boundary conditions (ABCs) for mesh truncation in the partial differential equation solution of electromagnetic scattering problems is briefly reviewed. The approximate 2-D ABC is compared with its exact counterpart and ways are suggested by which the ABCs can be improved. A direct application of the Wilcox expansion to the mesh truncation problem that bypasses the ABC altogether is discussed. The question of using a conformal (as opposed to cylindrical) outer boundary is addressed, and the ABC for this geometry is derived for 2-D scattering and guided wave problems. >

Radar scattering from bodies of revolution using an efficient partial differential equation algorithm

A technique is presented for solving the problem of scattering by a three-dimensional body of revolution using a partial differential equation (PDE) technique in conjunction with a radiation boundary condition applied in the Fresnel region of the scatterer. The radiation boundary condition, which is used to truncate the PDE mesh, is based on an asymptotic expansion derived by Wilcox (1956). Numerical results illustrating the procedure and verifying the accuracy of the results are included. >

PDE techniques for solving the problem of radar scattering by a body of revolution

The authors discuss two partial differential equation (PDE) techniques, namely the finite difference (FD) method and the finite element method (FEM), for solving the problem of radar scattering by a body of revolution (BOR). The formulation of the BOR problem is based upon the use of the coupled azimuthal potentials (CAPs), introduced by M.A. Morgan et al. (1977), that allow one to reduce the vector field problem to the solution of two coupled scalar wave equations. An approach to FD/FEM mesh truncation is developed on the basis of a multipole representation for the CAPs in the asymptotic region. Numerical results are presented for some representative geometries to illustrate the application of the PDE methods and some observations regarding the comparative performance of the two methods are included. >

Partial Differential Equation Methods for Solving the Problem of Electromagnetic Scattering from a Body of Revolution

Abstract In this paper we discuss the use of a local boundary condition derived from Wilcoxs expansion for the scattered fields to achieve mesh truncation for finite difference and finite element meshes. We review the method for the case of finite difference meshes and then show how it can be generalized for the case of a finite element mesh. We show how the finite element formulation can be developed without the use of a variational expression. We also present numerical results obtained using the finite element method.

An efficient numerical boundary condition for the truncation of finite element meshes for the analysis of electromagnetic scattering by complex bodies

The authors investigate the finite element implementation of a numerical boundary condition which, like the MEI (measured equation of invariance) boundary condition, depends on the location of the boundary node, the geometry of the scatterer, and the polarization of the incident field, and is derived by considering the fields that would be radiated by current sources in the vicinity of the scatterer. This boundary condition can be used for either homogeneous or inhomogeneous scatterers. This method of mesh truncation works well for both propagating and evanescent harmonics, even when the mesh boundary is quite close to the scatterer. Furthermore, it can be enforced on a mesh boundary of arbitrary shape; there is no requirement of a circular or spherical geometry. Numerical results obtained using this technique are presented.<<ETX>>

An efficient partial differential equation formulation for solving electromagnetic scattering from arbitrarily-shaped bodies of revolution

The authors consider the direct solution of the partial differential equations arising in the problem of electromagnetic scattering by an arbitrarily shaped perfectly conducting body of revolution (BOR). The BOR may. in general, be coated with one or more layers of dielectric material. The approach of R. Mittra and R.K. Gordon (1989) is generalized to arbitrarily shaped BORs by means of boundary-fitted curvilinear coordinates that avoid the problem of staircasing in the process of describing the geometry of the scatterer. As a numerical example, the authors consider the problem of a finite conducting cylinder, illuminated by a plane wave incident upon it.<<ETX>>