(Authors are listed in alphabetical order) Recently, the classical Waveform Relaxation (WR) approach was shown to be quite effective in solving the excessive runtime problem for multiple coupled transmission lines by a so-called transverse partitioning technique. The WR approach yields a remarkable linear increase in run time with respect to the number of lines. For some problems with more complex circuit topologies, additional splittings are desirable besides the transverse TL partitioning. This paper presents a new approach for the efficient longitudinal splitting for TEM mode transmission line problems. Previous longitudinal partitioning work using the classical WR for transmission lines led to limited solutions. This resulted in too many WR iterations and challenging partitioning problems. Here, we demonstrate a new optimized longitudinal WR algorithm for a single transmission line and determine an optimal choice of parameters. We give numerical examples to show the drastically improved convergence behavior
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