Finite-difference Green´s function diakoptics — Unlimited stable lookback schemes for non-trivial problems

Earlier, we have analysed a finite-difference timedomain (FDTD) toy problem for a configuration with two disjoint domains, each consisting of a single point, using a Green´s function diakoptics unlimited lookback scheme, based on the inverse of the stability function. We have developed an analogous scheme for non-trivial problems involving at least one interior point in one of the domains that occurs in the stability function, but does not enter directly into the boundary operator of the lookback scheme. This scheme preserves the stability. If self-consistency regarding the use of the proper discrete Green´s functions is maintained, the boundary operator remains restricted to the boundary. Otherwise the boundary operator fills up to become a domain operator, but may still be usable.