On the implementation and formulation of the electromagnetic surface integral equations

Abstract

Surface integral equation method is one of the most popular numerical methods in the computational electromagnetics. In this thesis three problem areas in the implementation and formulation of the frequency domain surface integral equation methods are studied.

First, a recursive technique is developed to evaluate the singular integrals arising from the electromagnetic surface integral equation methods. The technique is based on singularity subtraction method in which the most singular terms are extracted and evaluated analytically. A similar recursive algorithm is also developed for higher order basis functions. The technique is efficient and easy to apply for different surface integral equation formulations and polynomial basis functions.

The second problem is how to model the electromagnetic fields in complex structures. A procedure is developed for this junction problem to model the fields separately in each region and to properly enforce the electromagnetic boundary conditions on the interfaces of the regions. The developed method is very simple and independent of the surface integral equation formulation and thus makes it easy to apply to different formulations.

The third and most important problem is the choice of the electromagnetic surface integral equation formulation. Various traditional type of formulations are developed in this thesis and their behavior is studied especially with respect to the iterative methods.

The most significant part of this thesis is the new type of a surface integral equation formulation and new techniques developed for it. The main idea in this new formulation is to use the surface charge densities as unknowns in addition to the traditional surface current densities. The formulation does not have problems with the low frequencies, it is well-balanced and the convergence of the iterative methods is fast for a very wide frequency range. The new formulation seems to be the first well-conditioned, truly broadband formulation that can be used from static to high frequencies in a general case of composite metallic and dielectric structures.

The relation between the new formulation and the Picard's extended Maxwell system is also studied.