The development and characterisation of advanced nodes for the TLM method

Propagation of electromagnetic waves in three-dimensional (3D) space is studied using the Transmission-Line Modelling (TLM) method. The theoretical foundation, generalization and more advanced versions of the symmetrical condensed node (SCN), a basic structure for 3D TLM modelling, are presented. A unified approach to the derivation of TLM schemes capable of modelling nonuniform anisotropic materials on an arbitrarily graded mesh is introduced. The parameters and the scattering properties for a general symmetrical condensed node (GSCN) constructed from link lines with arbitrary characteristic impedances and up to six stubs are described. For the first time in 3D TLM modelling it is shown that stubs can be removed completely from the SCN, whilst still allowing general inhomogeneous problems to be modelled. This development, described as the symmetrical super-condensed node (SSCN), contributes significant reductions in memory storage and computer run-time in TLM simulations. In order to assess accuracy and numerical dispersion in the various TLM schemes based on the GSCN, dispersion relations are studied. A general approach for the analytical expansion of the general dispersion relation is introduced, enabling the derivation of dispersion relations in algebraic form for all currently available nodes. Based on the results obtained from the dispersion analysis, work aimed at constructing an optimal node is described. A class of adaptable symmetrical condensed nodes (ASCN) is derived, with superior propagation characteristics compared to other known TLM nodes