Starting from the equivalence theorem any composite metallic and dielectric structure can be analyzed by using SIE (surface integral equations). Such integral equations are usually solved by MoM (method of moments). Most of the existing MoM methods for solving SIE are developed for BORs (bodies of revolution). There are only few such methods that can handle structures of arbitrary shape. These methods use sub-domain basis functions defined over triangles, requiring a very large number of unknowns even for the simplest problems. This paper presents a new MoM method for electromagnetic modeling of composite metallic and dielectric structures. The method uses entire-domain basis functions defined over bilinear surfaces, resulting in a remarkably small number of unknowns.

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Electromagnetic Modeling of Composite Metallic and Dielectric Structures

Combined field integral equation (CFIE) is applied for computing electromagnetic scattering by arbitrarily shaped three dimensional dielectric and composite objects. The objectives of this paper are as follows. First, to present a CFIE formulation which can be used in the analysis of piecewise dielectric and composite metallic and dielectric objects with junctions. Second, to show that properly choosing the coupling coefficients of the equations the conditioning of the discretized matrix equation can be essentially improved and rapidly converging iterative solutions can be obtained even without preconditioning.

Application of combined field Integral equation for electromagnetic scattering by dielectric and composite objects

The surface integral equation method is applied for the electromagnetic analysis of general metallic and dielectric structures of arbitrary shape. The method is based on the EFIE-CFIE-PMCHWT integral equation formulation with Galerkins type discretization. The numerical implementation is divided into three independent steps: First,the electric and magnetic field integral equations are presented and discretized individually in each non-metallic subdomain with the RWG basis and testing functions. Next the linearly dependent and zero unknowns are removed from the discretized system by enforcing the electromagnetic boundary conditions on interfaces and at junctions. Finally,the extra equations are removed by applying the wanted integral equation formulation,and the reduced system is solved. The division into these three steps has two advantages. Firstly,it greatly simplifies the treatment of composite objects with multiple metallic and dielectric regions and junctions since the boundary conditions are separated from the discretization and integral equation formulation. In particular,no special junction basis functions or special testing procedures at junctions are needed. Secondly,the separation of the integral equation formulation from the two previous steps makes it easy to modify the procedure for other formulations. The method is validated by numerical examples.

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Surface Integral Equation Method for General Composite Metallic and Dielectric Structures with Junctions

We outline a generalized form of the method-of-moments technique. Integral equation formulations are developed for a diverse class of arbitrarily shaped three-dimensional scatterers. The scatterers may be totally or partially penetrable. Specific cases examined are scatterers with surfaces that are perfectly conducting, dielectric, resistive, or magnetically conducting or that satisfy the Leontovich (impedance) boundary condition. All the integral equation formulations are transformed into matrix equations expressed in terms of five general Galerkin (matrix) operators. This allows a unified numerical solution procedure to be implemented for the foregoing hierarchy of scatterers. The operators are general and apply to any arbitrarily shaped three-dimensional body. The operator calculus of the generalized approach is independent of geometry and basis or testing functions used in the method-of-moments approach. Representative numerical results for a number of scattering geometries modeled by triangularly faceted surfaces are given to illustrate the efficacy and the versatility of the present approach.

Generalized method of moments for three-dimensional penetrable scatterers

A new, general, and very efficient method for analysis of arbitrary composite metallic and dielectric structures, based on the PMCHW formulation and Galerkin method, is presented in this paper. Flexible geometrical modeling is performed by isoparametric surfaces (i.e., by bilinear surfaces in the particular case). Efficient approximation of currents is achieved by using polynomial entire-domain expansions (i.e., rooftop subdomain expansions in the particular case) that automatically satisfy the continuity equation, assuming that there are no line charges along surface edges. Special care is devoted to the treatment of arbitrary multiple metallic and/or dielectric junctions. Numerical results for different structures, obtained by using an extremely small numbers of unknowns, show very good agreement with other available data.

Electromagnetic modeling of composite metallic and dielectric structures

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.

J. Putnam

Papers

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