The "transmission-line matrix method" is a space and time discretising method for computation of electromagnetic fields. It is based on the analogy between the electromagnetic field and a mesh of transmission lines. The TLM method allows the computation of complex three-dimensional electromagnetic structures and has proven to be one of the most powerful time-domain methods along with the finite difference time domain method.
The TLM method is based on Huygens' model of wave propagation and scattering and the analogy between field propagation and transmission lines. Therefore it considers the computational domain as a mesh of transmission lines, interconnected at nodes. In the figure on the right is considered a simple example of a 2D TLM mesh with a voltage pulse of amplitude 1 V incident on the central node. This pulse will be partially reflected and transmitted according to the transmission-line theory. If we assume that each line has a characteristic impedance Z , then the incident pulse sees effectively three transmission lines in parallel with a total impedance of Z/3 . The reflection coefficient and the transmission coefficient are given by
The energy injected into the node by the incident pulse and the total energy of the scattered pulses are correspondingly
Therefore the energy conservation law is fulfilled by the model.
The next scattering event excites the neighbouring nodes according to the principle described above. It can be seen that every node turns into a secondary source of spherical wave. These waves combine to form the overall waveform. This is in accordance with Huygens principle of light propagation.
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