Hybrid Technique Combining the FDTD Method and Its Convolution Formulation Based on the Discrete Green´s Function

In this letter, a technique combining the finite-difference time-domain (FDTD) method and its formulation based on the discrete Green´s function (DGF) is presented. The hybrid method is applicable to inhomogeneous dielectric structures that are mutually coupled with wire antennas. The method employs the surface equivalence theorem in the discrete domain to separate the problem into a dielectric domain simulated using the FDTD method and a wire antenna simulated using the DGF formulation of the FDTD method. Therefore, both methods can be perfectly coupled without introducing any additional errors to the FDTD solution. Applications of the hybrid FDTD method are illustrated by two canonical problems involving half-wavelength dipole antennas and a dielectric object. If the DGF length is equal to the number of iterations in a simulation, the presented hybrid technique returns the same results as the direct FDTD method (assuming infinite numerical precision of computations).