Multi-Region Finite-Difference Time-Domain (MR-FDTD) Based on Domain-Optimal Green's Functions

Computational Electromagnetism

“…where or are spatially variable). For the wave equation the coupling of time domain boundary integral equation to an interior solver (either finite element or finite differences) is analyzed in [7] and a similar approach is proposed and tested in [52].…”

“…➋`D 1: Now we are given edge values L !.OEa i ; a j /, where OEa i ; a j stands for the edge connecting a i and a j . Adapting the idea from`D 0, in analogy to (52), we write an arbitrary line segment OEx; y T as a "weighted sum of edges of T", see Fig. 7: …”

Source decomposition as a global absorbing boundary condition for multi-region problems

“…Local ABCs are either derived from approximate one way equations [2,3,4,5] or absorbing conditions [6] and are applicable to non-reflecting external domains. Integral equationbased global methods [7,8] are quite suitable for this purpose since they can accommodate arbitrary external medium and tie in well with the interobject operator. The SDM is an integral ABC, however it is derived in a grid compatible manner from the difference equations rather than by a discretization of a continuous integral operator, as in [9].…”