Longitudinal-Partitioning-Based Waveform Relaxation Algorithm for Efficient Analysis of Distributed Transmission-Line Networks

In this paper, a waveform relaxation algorithm is presented for efficient transient analysis of large transmission-line networks. The proposed methodology represents lossy transmission lines as a cascade of lumped circuit elements alternating with lossless line segments, where the lossless line segments are modeled using the method of characteristics. Partitioning the transmission lines at the natural interfaces provided by the method of characteristics allows the resulting subcircuits to be weakly coupled by construction. The subcircuits are solved independently using a proposed hybrid iterative technique that combines the advantages of both traditional Gauss-Seidel and Gauss-Jacobi algorithms. The overall algorithm is highly parallelizable and exhibits good scaling with both the size of the network involved and the number of CPUs available. Numerical examples have been presented to illustrate the validity and efficiency of the proposed work.