Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media. I. Theory

Multilevel Fast Multipole Algorithm for Radiation Characteristics of Shipborne Antennas Above Seawater

“…ε i = ε i − jσ i /ω, µ i , and k i represent (in general complex) the permittivity, permeability, and wavenumber of the medium in which the target resides, and ω is the angular frequency (with a time dependence exp jωt assumed and suppressed). Details on the Green's function dyadicsḠ Aii andK Aii , as well as the scalar Green's function K ii φe have been given by Michalski and Zheng in [1], where we use their formulation C. The CFIE in (1) is valid for a more general layered medium [1], but here we only consider the half-space problem for simplicity.…”

“…The dyadic half-space Green's function is evaluated rigorously using the method of discrete complex images [23], thereby avoiding direct numerical evaluation of Sommerfeld integrals [1]. Impedance matrix elements representing these near interactions are stored in a sparse matrix called [Z near ].…”

“…Impedance matrix elements representing these near interactions are stored in a sparse matrix called [Z near ]. The method of complex images and explicit equations for the MoM impedance matrix elements can be found in literatures [1,23], and therefore, we do not repeat the details. …”

“…Since this far-field reflection coefficient approximation cannot account for surface waves, the MLFMA presented here is valid for targets situated entirely within a single source layer (not the general layered medium as in [1]). Therefore, in addition to the accurate calculation of the halfspace dyadic Green's function in the near interaction matrix [Z near ] (Section 2.1), the half-space MLFMA only requires the definition of a single set of real image sources (Fig.…”

“…Considering numerical modeling of such problems, there has been interest in method of moments (MoM) [1][2][3], finite-element method (FEM) [4] and finite difference time domain method (FDTD) [5,6]. The MoM, FEM and FDTD algorithms can handle such targets in principle, but memory requirements and computation time become excessive.…”