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 most successful methods can be categorized under the two following titles: (A) approximations to the continuous one way wave equation at the boundary e.g. the Engquist-Majda-Mur conditions [l], and (b) the use of artificial or physical absorbing materials near the boundary, such as the PML [2]. The ABC's, applied at the boundaries of the computational domain, are initially formulated in the continuous world, and then discretized for use in the FDTD scheme. It is now recognized that typically more than 10 PML layers must be employed for sufficiently accurate results. This extra computational region imposes additional burden on the computational resources, compared with simpler methods that only require a small stencil close to the boundary.