Unconditionally Stable Explicit Time-Domain Transmission-Line Matrix Method

This article presents the mathematical model of the unconditionally stable explicit transmission-line matrix (USE-TLM) method, which can operate at a time step beyond the Courant-Friedrichs-Lewy (CFL) limit. This technique is based on the eigenmode decomposition of the system matrix that represents the computational domain. Then, by eliminating all unstable modes, the system size is reduced and is usually much simpler to manipulate in terms of computational resources. Indeed, in practical simulations, the number of modes one should conserve is very small compared to when the entire set of eigenmodes is considered. This procedure can considerably reduce the size of the system matrix leading to some substantial computational gain as compared to the traditional TLM method. Finally, some issues regarding the accuracy of the proposed technique are investigated. Several numerical experiments are presented and comparisons with other approaches show the validity and the performance of the proposed TLM procedure.