@article{2239ebc2a4b44274bc092cc7d4214da4,
title = "On the convergence of the classical symmetrical condensed node-TLM scheme",
abstract = "This paper presents a proof of convergence of the transmission-line matrix (TLM) method with a symmetrical condensed node (SCN) in the classical formulation of Johns. It is shown that the convergence order of the SCN-TLM method cannot simply be derived from observing the dispersion characteristics of the TLM mesh. The mapping between the discretized electromagnetic field and TLM wave amplitudes plays a decisive role. Although second-order convergence is observed for coarse discretizations, which are usually used in practice due to the limitations of memory resources, it is shown and numerically verified that the asymptotic convergence reduces to order O(√Δt). Only using a bijective field mapping defined at the cell boundaries yields second-order convergence.",
author = "Rebel, {J{\"u}rgen N.} and Martin Aidam and Peter Russer",
note = "Funding Information: Manuscript received August 11, 1999. The work of J. N. Rebel and M. Aidam was supported by Siemens AG under an Ernst-von-Siemens Scholarship. J. N. Rebel was with the Institut f{\"u}r Hochfrequenztechnik, Technische Uni-versit{\"a}t M{\"u}nchen, D-80333 Munich, Germany. He is now with the Wireless Group, Infineon Technologies AG, D-81541 Munich, Germany. M. Aidam was with the Institut f{\"u}r Hochfrequenztechnik, Technische Univer-sit{\"a}t M{\"u}nchen, D-80333 Munich, Germany. He is now with Daimler Chrysler, D-71059 Sindelsingen, Germany. P. Russer is with the Institut f{\"u}r Hochfrequenztechnik, Technische Universit{\"a}t M{\"u}nchen, D-80333 Munich, Germany. Publisher Item Identifier S 0018-9480(01)03321-X.",
year = "2001",
doi = "10.1109/22.920154",
language = "English",
volume = "49",
pages = "954--963",
journal = "IEEE Transactions on Microwave Theory and Techniques",
issn = "0018-9480",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "5",
}