Longitudinal partitioning based waveform relaxation algorithm for transient analysis of long delay transmission lines

In this paper a waveform relaxation algorithm based on longitudinal partitioning is presented to efficiently model large distributed networks. The proposed methodology represents lossy transmission lines as a cascade of lumped circuit elements and lossless line segments, where the lossless line segments are modeled using the method of characteristics. This allows the transmission line to be naturally partitioned into smaller, weakly coupled subcircuits, enabling the waveform relaxation algorithm to converge more efficiently compared to existing relaxation algorithms based on longitudinal partitioning using the conventional lumped model. A numerical example is provided to demonstrate the validity of the proposed algorithm.