A method for calculating the electromagnetic scattering from and internal field distribution of arbitrarily shaped, inhomogeneous, dielectric bodies is presented. A volume integral equation is formulated and solved by using the method of moments. Tetrahedral volume elements are used to model a scattering body in which the electrical parameters are assumed constant in each tetrahedron. Special basis functions are defined within the tetrahedral volume elements to insure that the normal electric field satisfies the correct jump condition at interfaces between different dielectric media. An approximate Galerkin testing procedure is used, with special care taken to correctly treat the derivatives in the scalar potential term. Calculated internal field distributions and scattering cross sections of dielectric spheres and rods are compared to and found in agreement with other calculations. The accuracy of the fields calculated by using the tetrahedral cell method is found to be comparable to that of cubical cell methods presently used for modeling arbitrarily shaped bodies, while the modeling flexibility is considerably greater.

A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies

Simple and efficient numerical methods are developed for treating electromagnetic problems of scattering and radiation from surfaces. Special consideration is given to the treatment of edges so that rather arbitrary geometrical configurations may be handled. For the conducting body problems considered, an electric field integral formulation is used, and the method of moments is applied using pulse expansions to represent both the current and the charge. It is demonstrated that proper placement of the current and charge subdomains relative to edges not only is important in treating edges but also yields a convenient numerical procedure. A simple testing scheme is used which is almost as efficient as point-matching. Numerical results indicate that the approach is free of anomalies in the behavior of current near edges and of other previously observed numerical instabilities. Problems considered include conducting strips (both TM and TE), a bent rectangular plate, and both material and conducting bodies of revolution.

Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces

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

We present an accurate method of moments (MoM) solution of the combined field integral equation (CFIE) using the multilevel fast multipole algorithm (MLFMA) for scattering by large, three-dimensional (3-D), arbitrarily shaped, homogeneous objects. We first investigate several different MoM formulations of the CFIE and propose a new formulation, which is both accurate and free of interior resonances. We then employ the MLFMA to significantly reduce the memory requirement and computational complexity of the MoM solution. Numerical results are presented to demonstrate the accuracy and capability of the proposed method. The method can be extended in a straightforward manner to scatterers composed of different homogeneous dielectric and conducting objects.

Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies

The recent development and extension of the method of moments technique for analyzing electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects is presented based on the combined field integral equations. The surfaces of the homogeneous three-dimensional arbitrary geometrical shapes are modeled using surface triangular patches, similar to the case of arbitrary shaped conducting objects. Further, the development and extensions required to treat efficiently three-dimensional lossy dielectric objects are reported. Numerical results and their comparisons are also presented for two canonical dielectric scatterers-a sphere and a finite circular cylinder.

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R. F. Harrington

Papers

Electromagnetic scattering from a homogeneous material body of revolution