Spatial interpolation method for solution of electromagnetic scattering from objects located in half-space

Efficient evaluation of spatial Green´s functions is a key to solve radiation and scattering from the objects located in half-space by integral equation method. In this paper, tabulation and interpolation for Sommerfeld integrals are discussed to calculate spatial Green´s functions for half-space. If the object is located in the same half-space, a 2D interpolation scheme is requested; if penetration occurs, 3D one is requested. In order to reduce the number of sampling points and to obtain better accuracy, a modified interpolation technique is employed to smoothen the interpolated functions from which an oscillatory term or a singular factor is extracted out. Since the proposed method makes the best of the slowly varying spatial characteristics, spatial repetition and cylindrical symmetry of the spatial Green´s functions, tremendous computation effort is avoided as well as efficiency of impedance matrix filling is enhanced.