R. Holtzman et R. Kastner, The time-domain discrete Green's function method (GFM) characterizing the FDTD grid boundary, IEEE ANTENN, 49(7), 2001, pp. 1079-1093
For a given FDTD simulation space with an arbitrarily shaped boundary and a
n arbitrary exterior region, most exisitng absorbing boundary conditions be
come inapplicable, A Green's function method (GFM) is presented which accom
modates arbitrarily shaped boundaries in close proximity to a scattering ob
ject and an arbitrary composition in the exterior of the simulation space.
Central to this method is the numerical precomputation of a Green's functio
n tailored to each problem which represents the effects of the boundary and
the external region. This function becomes the kernel for a single-layer a
bsorbing boundary operator. It is formulated in a manner which naturally in
corporates numerically induced effects, such as the numerical dispersion as
sociated with the FDTD scheme, The Green's function is an exact absorber in
the discretized space, This property should be contrasted with other metho
ds which are initially designed for the continuum and are subsequently disc
retized, thereby incurring inherent errors in the discrete space which cann
ot be eliminated unless the contiuum limit is recovered. In terms of accura
cy, the GFM results have been shown to be of a similar quality to the PML,
and decidedly superior to the Mur condition. The properties of the GFM are
substantiated by a number of numerical examples in one, two, and three dime
nsions.