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

A novel double higher order Galerkin-type method of moments based on higher order geometrical modeling and higher order current modeling is proposed for surface integral equation analysis of combined metallic and dielectric antennas and scatterers of arbitrary shapes. The technique employs generalized curvilinear quadrilaterals of arbitrary geometrical orders for the approximation of geometry (metallic and dielectric surfaces) and hierarchical divergence-conforming polynomial vector basis functions of arbitrary orders for the approximation of electric and magnetic surface currents within the elements. The geometrical orders and current-approximation orders of the elements are entirely independent from each other, and can be combined independently for the best overall performance of the method in different applications. The results obtained by the higher order technique are validated against the analytical solutions and the numerical results obtained by low-order moment-method techniques from literature. The examples show excellent accuracy, flexibility, and efficiency of the new technique at modeling of both current variation and curvature, and demonstrate advantages of large-domain models using curved quadrilaterals of high geometrical orders with basis functions of high current-approximation orders over commonly used small-domain models and low-order techniques. The reduction in the number of unknowns is by an order of magnitude when compared to low-order solutions.

https://www.engr.colostate.edu/~notaros/Papers/T-AP_Aug_2004.pdf

Double higher order method of moments for surface integral equation modeling of metallic and dielectric antennas and 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

A higher order multilevel fast multipole algorithm (MLFMA) is presented for computing electromagnetic scattering from three-dimensional bodies comprising both conducting and dielectric objects. The problem is formulated using the Poggio-Miller-Chang-Harrington-Wu-Tsai (1973, 1977) approach for multiple homogeneous dielectric objects and the combined-field approach for conducting objects. The resultant integral equations are discretized by the method of moments (MoM), in which the conducting and dielectric surfaces/interfaces are represented by curvilinear triangular patches and the unknown equivalent electric and magnetic currents are expanded using higher order vector basis functions. Such a discretization yields a highly accurate representation of the unknown currents without compromising the accuracy of geometrical modeling. An implicit matrix-filling scheme is employed to facilitate the treatment of complex scatterers having multiple junctions. The resultant numerical system is then solved by MLFMA, which is tailored to accommodate the material properties of dielectric scatterers, and the solution is accelerated using an incomplete LU decomposition preconditioner. Numerical examples are presented to demonstrate the accuracy and versatility of this approach in dealing with a wide array of scattering problems.

A higher order multilevel fast multipole algorithm for scattering from mixed conducting/dielectric bodies

This paper deals with the problem of the calculation of surface integrals for electromagnetic scattering in the case of the widely popular double-triangular basis functions first introduced by Rao, Wilton, and Glisson (1982). An entire set of formulas is obtained which overrides the difficulties inherent to the singularity of the integrands, and results showing the stability, accuracy, and efficiency of the methods developed are reported in an application of the method of moments to the case of perfectly conducting surfaces and computation of near field in domains including the surface itself. Furthermore, the authors provide insight as regards the capability of triangular basis functions to model near field patterns. >

Theoretical and numerical treatment of surface integrals involving the free-space Green's function

An efficient and accurate numerical procedure for the analysis of the electromagnetic scattering and radiation from arbitrarily shaped, composite finite conducting and dielectric bodies is proposed. A set of coupled electric field integral equations involving surface equivalent electric and magnetic currents is used. The coupled integral equations are solved through planar triangular patch modeling and the method of moments. Two separate, mutually orthogonal vector functions for each edge connecting a pair of triangular patches have been developed. Numerical results for disk/cone and cylinder/cone structures are compared with other available data. Limited comparison with experimental data has also been made. >

A.R. Djordevic

Papers

Electromagnetic radiation and scattering from finite conducting and dielectric structures: surface/surface formulation