On the convergence of the classical symmetrical condensed node-TLM scheme

This paper presents a proof of convergence of the transmission-line matrix (TLM) method with a symmetrical condensed node (SCN) in the classical formu lation of Johns. It is shown that the convergence order of the SCN-TLM meth od cannot simply be derived from observing the dispersion characteristics o f the TLM mesh, The mapping between the discretized electromagnetic field a nd TLM wave amplitudes plays a decisive role. Although second-order converg ence is observed for coarse discretizations, which are usually used in prac tice due to the limitations of memory resources, it is shown and numericall y verified that the asymptotic convergence reduces to order O(root Deltat). Only using a bijective field mapping defined at the cell boundaries yields second-order convergence.