Efficient Incorporation of a PEC/PMC Plane in the Multiple-Grid Adaptive Integral Method

The multiple-grid adaptive integral method (MG-AIM) is extended for fast analysis of scattering from piecewise homogeneous structures on or above a perfect electrically/ magnetically conducting plane. Because the Green functions in the relevant integral equations contain (i) reflection terms that are in correlation form in the direction normal to the plane and (ii) direct terms that are in convolution form in all directions, the MG-AIM propagation stage gives rise to Hankel-(two level) block-Toeplitz matrices in addition to the usual (three level) block-Toeplitz matrices. These additional matrices are multiplied with trial vectors during the iterative solution stage by using FFTs; however, to improve efficiency, the FFTs computed for multiplying the direct terms are recycled. Numerical examples show that the proposed method requires (almost) half the number of computations and storage space compared to a brute-force imaging scheme for structures that terminate on the plane; larger gains are observed for structures residing above the plane.