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

Abstract

For a given FDTD simulation space with an arbitrarily shaped boundary and an arbitrary exterior region, most existing absorbing boundary conditions become inapplicable. A Green's function method (GFM) is presented which accommodates arbitrarily shaped boundaries in close proximity to a scattering object and an arbitrary composition in the exterior of the simulation space. Central to this method is the numerical precomputation of a Green's function tailored to each problem which represents the effects of the boundary and the external region. This function becomes the kernel for a single-layer absorbing boundary operator, it is formulated in a manner which naturally incorporates numerically induced effects, such as the numerical dispersion associated with the FDTD scheme. The Green's function is an exact absorber in the discretized space. This property should be contrasted with other methods which are initially designed for the continuum and are subsequently discretized, thereby incurring inherent errors in the discrete space which cannot be eliminated unless the continuum limit is recovered. In terms of accuracy, the GFM results have been shown to be of a similar quality to the PML, and decidedly superior to the Mur (1981) condition. The properties of the GFM are substantiated by a number of numerical examples in one, two, and three dimensions.