ABSTRACT
It is always difficult to decide on a logic of presentation and it is certain that any approach will not satisfy all. It is therefore our intention to make clear at this stage how we propose to progress. In the first instance, we will discuss 1-D (1-D) TLM algorithms. Considerable progress can be achieved without going too deeply into the fundamental theory. Suffice to say that until recently such algorithms were based on an assumption that the diffusion equation could be modeled using the telegraph equation under conditions where space and time discretization allowed the wave component to be neglected (the basis of this will be addressed in the theory section). The next section extends algorithm development to two and three dimensions, but a discussion on the types of excitation will be reserved for the section after, which will include some new material. At this point, we are in a position to discuss some practical implementations of thermal and particle diffusion. Once all of this is in place, we will present some supporting theory. This has been covered in considerable detail elsewhere and for that reason
this final section will be concerned with recent developments in our understanding of the underlying processes that influence the development and implementation of TLM algorithms. The presentation of some advanced theory and applications will be held over for the final chapter.
