A Robust Integral Equation Solution for EM Scattering by a Plate in Conductive Media

Abstract

A new integral solution formulated with the Galerkin method is derived and applied to model the electromagnetic response of a thin conducting plate in a stratified medium. The solution is expressed as two coupled integral equations, one for the scalar potential of the equivalent current density and the other for the corresponding magnetic field. The solution adopts the form of a single equation plus a constraint on the current density in two limiting cases. Where the host medium is resistive, the scalar potential equation forces the current to be divergence free. For static field excitation, the magnetic field equation forces the current to be curl free. This property of the solution is responsible for the robustness of the method for a wide range of model parameters. The Galerkin method requires multiple integration which can be extremely time-consuming when the required Green function is not analytical. To overcome this problem, new integration techniques are introduced in which the Green function is represented as a product of geometrical and electrical factors. The geometrical factors are time-consuming to calculate but can be pre-calculated and used in many model evaluations. The electrical factor can be computed relatively easily, but cannot be saved. This separation permits the response of the plate in a layered environment to be calculated extremely efficiently. Parametric scaling arguments are used to determine when it is necessary to compute the EM response with a solution accounting for both galvanic and inductive effects. Estimators are developed and tested which allow one to predict if the complete solution to be replaced by simpler solutions such as those which treat the inductive and galvanic components separately. These estimators may be used to predict the mode of current excitation itself, or the mode of current excitation which dominates the sensed fields.