The time-domain discrete Green's function method (GFM) characterizing the FDTD grid boundary

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.