On the Aspects of Selecting the Symmetrical Condensed Node or the Expanded Node Modelling for Electromagnetic Simulations

In view of recent research showing equivalence between various versions of the FD-TD and TLM methods we propose that comparative studies of time - domain methods be now directed towards distinguishing Expanded Node modelling and Symmetrical Condensed Node modelling. Each of these types of modelling can be used to formulate algorithms in either FD-TD or TLM notations. The choice of notation influences effectiveness of the analysis, but accuracy is essentially determined by the type of modelling. We derive an analytic function which describes dispersion relations for the Symmetrical Condensed Node (SCN) modelling. Our formulation provides the unprecedented basis for thorough comparison with the expanded node modelling, in terms of overall accuracy, reliability and convergence properties. Theoretical predictions are verified on several examples. Detailed examination of inherent computational efficiency of the ExpN and SCN models for 2-D, 2-DV and 3-D problems is supplemented.