EM MODELLING USING SURFACE INTEGRAL EQUATIONS1

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Abstract
The theory by which the Surface Integral Equation method may be applied to the solution of electromagnetic transmission boundary value problems is presented. For a 3D target of arbitrary electrical property contrast with its host medium excited by an arbitrary time‐harmonic source, two integral equations are derived which need to be simultaneously solved for tangential electric and magnetic source density on the target's surface. If the target is 2D, though still excited by an arbitrary source (the 2½ D case), the problem is best solved in the transform domain for a number of different wavenumbers in the target's strike direction. Then a set of four simultaneous scalar integral equations needs to be solved for the components of the surface source density transforms in the target's strike direction and in the direction of the tangent vector to the target's cross‐sectional contour.Examples are presented in which the 2½D problem is solved numerically using the method of moments with piecewise linear basis functions. Although the results generally compare well with analytical solutions, or solutions obtained numerically by other means, errors appear in the calculation of the real response of these targets to excitation by a magnetic dipole source at low frequencies. This is attributed to ill‐conditioning of the system resulting from a non‐unique solution at zero frequency.