Solution of large transmission line type circuits using a new optimized waveform relaxation partitioning

Large problems can be solved with the ever increasing availability of computing power. However, our ability to solve large circuit and transmission line problems, in the time domain, is still relatively modest. Partitioning into a set of smaller problems is essential for the electrical modeling of very large systems. However, so far the partitioning of strongly coupled circuits like transmission lines has been difficult. We introduce a new approach for coupling partitioned problems in the context of waveform relaxation methods, which leads to the class of optimized waveform relaxation algorithms with greatly enhanced performance. We analyze convergence for the case of a transmission line type circuit and illustrate the method with several quasi TEM mode transmission line problems.