### Transmission Line Matrix Method

Transmission Line Modelling (TLM) or Transmission Line Matrix (TLM) Modelling (depending on who you ask) is a general numerical simulation technique suitable for solving field problems. Its main application has been in electromagnetics, but it has also been applied to thermal or diffusion problems as well as acoustics.

The TLM method belongs to the general class of differential time-domain numerical modelling methods. The basic approach of the TLM method is to obtain a discrete model which is then solved exactly by numerical means; approximations are only introduced at the discretisation stage. This is to be contrasted with the traditional approach in which an idealized continuous model is first obtained and then this model is solved approximately. For electromagnetic systems, the discrete model is formed by conceptually filling space with a network of transmission-lines in such a way that the voltage and current give information on the electric and magnetic fields. The point at which the transmission-lines intersect is referred to as a node and the most commonly used node for 3D work is the symmetrical condensed node. At each timestep, voltage pulses are incident upon the node from each of the transmission-lines. These pulses are then scattered to produce a new set of pulses which become incident on adjacent nodes at the next timestep. The relationship between the incident pulses and the scattered pulses is determined by the scattering matrix, which is set to be consistent with Maxwell's equations. Additional elements, such as transmission-line stubs, can be added to the node so that different material properties can be represented.

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