Field theoretical foundations of the two-dimensional TLM method and the three-dimensional TLM method with condensed node are given using the method of moments with sectional base functions. Introducing the Hilbert space representation for the field state, the description of geometrical structures and the field evolution is performed algebraically. It is shown that the sampling of the tangential electric and magnetic field components in the cell boundary surfaces yields a correct bijective mapping between electromagnetic field components and TLM wave amplitudes. The same method is applied to derive the two-dimensional and three-dimensional FDTD schemes. For the calculation of the TLM and FDTD dispersion relations, we use a new generalized method. A critical comparison of two-dimensional and three-dimensional TLM with Yee's finite difference time domain method is given.     «

Field theoretical foundations of the two-dimensional TLM method and the three-dimensional TLM method with condensed node are given using the method of moments with sectional base functions. Introducing the Hilbert space representation for the field state, the description of geometrical structures and the field evolution is performed algebraically. It is shown that the sampling of the tangential electric and magnetic field components in the cell boundary surfaces yields a correct bijective mappin...     »