Source Decomposition as a Diakoptic Boundary Condition in FDTD With Reflecting External Regions

The diakoptic approach is utilized for the creation of boundary conditions for the truncation of the FDTD computational grid in the presence of reflecting external media. The interfaces between the regions can be of arbitrary shape and are in close proximity to the scatterers in both regions. Surface Green's functions over these interfaces serve to characterize the external domain from a viewpoint of the computational domain. Previously used field definitions of such Green's functions, that can be viewed as analogs of parameters in microwave networks, have involved effective hard boundaries at the interfaces. These boundaries, however, can cause artificial interactions with physical reflecting bodies in the external domain. To eliminate this phenomenon, the Green's functions are now defined in terms of outgoing and incoming wave constituents, rather than fields. This distinction between the aforementioned constituents is made by viewing them as originating from sources within and outside the computational domain. The Green's function-based boundary conditions are demonstrated to operate successfully in the two-dimensional case, resolving the aforementioned resonance issues efficiently and accurately.