Numerical Analysis in Electromagnetics: The TLM Method

Chapter 2

3D Nodes

2.1. Historical development

2.1.1. Distributed nodes

The nodes used in 2D [JOH 71, HOE 91] were combined into a distributed node which would enable 3D simulation. This node, as presented by Akhtarzad and Johns [AKH 74], is achieved by the interconnection of three series nodes and three parallel nodes, which thus form a cube with edges of length Δl/2 (Figure 2.1). The equivalent electrical scheme of the distributed node is given by [AKH 75]. The theory and the whole package of applications of these schemes are brought together in a review paper proposed by Hoefer [HOE 85]. The diverse components of the electromagnetic field are thus available at the corners of the cube, at the parallel nodes for the electrical field and at the series nodes for the magnetic field. The connection of multiple nodes of this type enables the simulation of a 3D medium.

The topology of the distributed node is similar to that of the FDTD for the Yee cell [YEE 66]. The advantage of the TLM approach is in the fact that we are making use of three out of six field components at each scattering point (the point where the transmission lines intersect on the scheme) against just one for FDTD. However, the distributed node requires twice as many variables as the FDTD cell. Furthermore, the major disadvantage of this node is the complexity of its numerical scheme [JOH 87]; the fields calculated at the scattering points are spatially separated and are therefore not instantly updated. This makes ...