Mesh optimisation methods for unstructured transmission-line modelling

Transmission-line modelling (TLM) is a valuable technique for numerical simulation of electromagnetic fields. Recently, investigations have been successfully carried out into the use of the TLM approach on unstructured meshes However, as the local characteristics of mesh geometry will clearly make an impact upon the fidelity of simulations, it is necessary to examine suitable techniques for mesh optimisation. Three different methods have been investigated here to find optimal meshes for subsequent TLM simulations: the centroidal Voronoi Tessellation method, the optimal Delaunay triangulation method and a spring relaxation method. These different techniques are assessed in terms of maximum efficiency of the subsequent TLM simulations and the computational cost that is incurred to identify them. Several different canonical examples of mesh are considered to determine the generality of the conclusions drawn.