TLM Local Mesh-Refinement Scheme Based on N-Port Network Representation and Conference-Matrix Connection Topology

This article presents an optimal connection topology to model the voltage-exchange at the interface between different sub-grids in nonstructured TLM meshes. As a first step, the derivation—using Kirchhoff's circuit laws—of these voltage-exchange equations between two subdomains with an arbitrary meshing ratio and a specific connection topology is presented. It was then generalized as an S-matrix of an N-port network that processes all desired properties in an ideal interface. In contrast to previous approaches, these S-matrix elements are derived directly for their properties and no concrete physical representation is required. Moreover, stability in this novel connection topology is ensured since all eigenvalues of the optimal S-matrix are located on the unit circle.