FDTD simulations on disjoint domains with the use of discrete Green's function diakoptics

Abstract

A discrete Green's function (DGF) approach to couple disjoint domains in the finite-difference time-domain (FDTD) grid is developed. In this method, total-field/scattered-field (TFSF) FDTD domains are associated with simulated objects whereas the interaction between them is modeled with the use of the DGF propagator. Hence, source and scatterer are simulated in separate domains and updating of vacuum cells, being of little interest, can be avoided. The simulation scenarios consisting of (i) disjoint domains separated by a spatial distance and (ii) a sub-domain embedded in the main grid are considered. In the developed method, the field radiated by an FDTD domain is computed as a convolution of DGF with equivalent current sources measured over two displaced Huygens surfaces in the scattered-field zone. Therefore, the computed electromagnetic field is compatible with the FDTD grid and can be applied as an incident wave in a coupled TFSF domain. The developed method of diakoptics can be generalized for simulations of FDTD domains requiring nonlinear or multiphysics modeling with interaction between them computed with the use of DGF propagators.