Transmission-line modeling (TLM) based upon unstructured tetrahedral meshes

This paper presents a transmission-line modeling (TLM) algorithm, which is based upon unstructured tetrahedral meshes. In comparison with the conventional, usually Cartesian, scheme, the use of such meshes provides a significant enhancement in the flexibility and accuracy of the TLM simulations, permitting both smooth boundary approximations and the use of diversely sized elements in multiscale problems. A full theoretical development of the unstructured algorithm is presented for the first time and canonical problems are used to demonstrate the computational advantages available. Particular consideration is given to practical meshing constraints and the merging of adjacent tetrahedra into larger cells used to avoid the use of undesirably small time steps.