4.1 INTRODUCTION

The objective of this chapter is to review briefly the classical modal solutions for 2-D cylinders and spheres and then to examine the powerful numerical techniques used to solve Maxwell s equations as expressed by the Stratton-Chu integral formulations and the differential equation formulations.

Exact solutions for practical geometries for scattering are rarely found. This is because the wave equation is solvable by historical analytical methods when the scattering geometry coincides with one of the few separable coordinate systems for which exact series solutions are available. Unfortunately, few practical geometries match the solutions available.

Computer solutions started to gain momentum in the late 1960s after publication of Harrington s [1] classic book on using the method of moments to solve the integral formulation of Maxwell s equations. Until then this formulation was considered only of theoretical interest because we could obtain no practical solutions.

A principal objective of solving Maxwell s equations is to predict the RCS scattering behavior. Although this is certainly a valid objective, we also need to use our solutions to gain an appreciation of the scattering process. Therefore we should also ask our tools to show phenomenological results of how an electromagnetic wave interacts with a scattering body. Hence, surface currents and near fields are of interest. Imaging, using analytical and computer codes, should also be pursued to gain understanding of scattering mechanisms and spatial regions on the bodies that produce a scattered field.

Differential equation numerical techniques are now developing rapidly and for certain classes of...