The time domain discrete Green's function method (GFM) as an ABC for arbitrarily-shaped boundaries

With the advent of newly-introduced absorbing boundary conditions (ABC's) for mesh truncation in the context of the finite-difference-time-domain (FDTD) computations, it has been recognized that the boundaries of the computational domain can be defined in close proximity to scatterers, and yet produce very small reflections. The time-domain Green's function of the external region beyond a given boundary, presented here, is an inherently discretized version of the impedance condition. It is incorporated in a single layer boundary condition, termed the Green's function method (GFM), whereby the effect of the external region has been replaced by a convolution summation over the boundary alone. The development is carried out entirely within the framework of the general, discrete space-time domain grid rather than relying on the discretization of continuous relationships. Hence, it includes the effects of finite sampling, such as the presence of numerical dispersion and potential instabilities, as one of its main features.