Transmission-Line Modeling Using Unstructured Triangular Meshes

Some key developments in computational electromagnetics and their attribution

“…TLM is now a well established technique for modeling EM problems [74], although current implementations are restricted to structured Cartesian meshes. Unstructured meshes offer better versatility for mapping complex geometries and hence current effort is directed to develop TLM algorithms capable of working with these types of unstructured triangular meshes [75]. Unstructured meshes are particularly beneficial where a range of feature sizes need to be accurately modeled and easily lend them to nonuniform meshing, employing the necessary computational resources around small features whilst minimizing computational effort in the empty spaces.…”

A hybrid Boundary Element Unstructured Transmission-line (BEUT) method for accurate 2D electromagnetic simulation

“…Unfortunately just like the structured TLM, the UTLM method requires the use of Approximate Boundary Conditions (ABCs) to model the radiating behaviour of the fields at the boundary of the simulation domain. Moreover, for these ABCs to be accurate, the simulation domain needs to be extended beyond the domain occupied by the device under study, leading to an increase in the size of the problem and thus an increase in solution time [6,7]. Finally, the ability to model plane wave excitations and compute radar cross sections, though possible, is not immediately available using TLM [8].…”

“…The TLM method is an established time-domain numerical simulation tool which until 2005 [7] In [7], such a circuit is designed for unstructured triangular domains where the Dirichlet-to-Neumann map for a small triangular region can be approximated to first order accuracy by a network of transmission lines with the signal transit time along all transmission lines synchronized to the discretization timestep; i.e. a commensurate network is created.…”

“…3b. In order to match the inductive and capacitive response of the circuit to that of the medium, link and stub admittances need to be chosen as derived in [7],…”

“…To ensure that a stable algorithm is created and a physically reasonable timestep is chosen, Delaunay triangular meshes must be used, as explained in [7], where the link line lengths will never be negative. An example mesh with the corresponding link lines is shown in fig.…”