The transmission line matrix method, or TLM [4,29,90] appeared a bit later, in the early 1970s [97,100]. It (like the wave digital filtering approach) is a descendant of the ground-breaking work of Kron , who developed circuit models of electromagnetic field problems before the widespread availability of electronic computers. TLM is very similar to the DWN, in that it employs a network of discrete transmission lines connected at scattering junctions in order to simulate the behavior of a distributed system. The first formulation, known as the expanded node formulation was derived from a lumped (RLC) model of the (2+1)D transmission line equations , and is identical to the type III DWN we will present in §4.3.6. TLM has developed in numerous ways since its inception; the most significant thrust has been towards formulations for which the various field components are not staggered, but computed together at larger nodes. The symmetric condensed node  and its numerous offspring, such as the hybrid symmetrical condensed node  are the results of this work.
FDTD and TLM have been compared and linked in various ways [38,98], most significantly through the use of field expansions , and new variants of FDTD have been developed using TLM as a starting point . We will take a different approach here. Beginning from the observations that have been made regarding the equivalence of certain DWNs to difference methods [67,157,198,200] we will show that Yee's algorithm is equivalent to a family of scattering structures, some of which appear to be quite different from those that have been proposed in the TLM literature. The correspondence holds for media with spatially-varying material parameters; numerical integration of the equations defining such materials has not, as yet, been approached using DWNs. We also note that the TLM community appears to be aware neither of the many valuable numerical properties which scattering-based numerical methods possess [46,165], in particular their behavior in finite arithmetic, nor of other useful signal-processing manipulations (such as power-normalization of wave quantities and dynamic range minimization ) which have their roots in electrical network theory.