X. Gui et al., A GENERAL EXPRESSION OF BOUNDARY-CONDITIONS IN TLM DIFFUSION MODELING, International journal of numerical modelling, 9(6), 1996, pp. 459-461
We show that the general boundary condition D partial derivative Phi/p
artial derivative x + alpha Phi = 0 (D is the diffusion coefficient an
d alpha is a constant) in TLM diffusion modelling can be expressed acc
urately in terms of a voltage reflection coefficient rho = (Delta x -
alpha Delta t)/(Delta x + alpha Delta t), where Delta x is the spatial
resolution and Delta t is the time step. Based on this general expres
sion, the special cases of short-circuit (rho = -1), open-circuit (rho
= 1) and matched-load (rho = 0) boundaries can be described succinctl
y by alpha --> infinity, alpha --> 0 and alpha = Delta x/Delta t, resp
ectively. This formulation allows for straightforward treatment of mix
ed boundary conditions found, for example, in diffusion-drift systems.