Computing TLM symmetrical nodes in a unified FDTD fashion

The transmission line matrix (TLM) method has been shown to be an effective means for solving electromagnetic problems. Various TLM nodes have been developed with different stability conditions and dispersion characteristics. In this paper, a general FDTD scheme equivalent to all the TLM nodes is developed. The scheme involves central finite-differencing of Mar,tell's equations at the center of a cell and an averaging process at the boundary surfaces of the cell. The variations of the weighting coefficients in the averaging schemes result in the equivalence of the FDTD method to different TLM nodes such as SCN and SSCN nodes. As a result, the TLM nodes is generally unified under and formerly made equivalent to a finite-different time-domain method. In other words, ail the available TLM nodes can be computed in a FDTD fashion where Maxwell's equations are explicitly expressed and implementations of the modelling schemes such as Perfectly Matched Layer can be made very easily