Integral equations with reduced unknowns for the simulation of two-dimensional composite structures

A set of integral equations with reduced unknowns is derived for modeling two-dimensional inhomogeneous composite scatterers. The scatterer is first simulated in terms of thin curvilinear material layers of constant thickness. The traditional integral equations corresponding to each inhomogeneous layer are then manipulated in a manner allowing the identification of a new equivalent current component to replace two of the traditional ones across the layer. The given integral equations require approximately 2N current-component unknowns for their numerical implementation instead of the 3N unknowns generally required with traditional formulations. The implied computational efficiency though, was obtained at the expense of some complexity in the resulting pair of integral equations. To test the validity of the derived integral equations, special attention is given to a moment-method implementation of the authors' compact set of integral equations, with emphasis on the analytical evaluation of the diagonal and near-diagonal elements of the impedance matrix. Scattering patterns are presented as computed with the compact set of integral equations. These are further compared with measured data and computations using alternate analytical techniques. In all cases, these were in excellent agreement with corresponding results achieved by alternate methods.<>