Appendix A

Development of Maxwell’s Equations using the Z Transform with a Variable Mesh

Maxwell’s equations are written (without considering sources) as follows:

– First equation: − rot in-appa-image147-01.gif


For normalized field values, we obtain:


Knowing that Δl = 2 c Δt, and following simplification, we obtain:


In order to be able to use the traditional TLM algorithm, the term in-appa-image149-01.gif is added to both sides of each equation:


We can see that each part of this set of equations is simplified and can be integrated into the classic TLM process. It only remains for us to develop the second part. For example, for the first line, we obtain:


Knowing that in-appa-image150-01.gif, this second term is then expressed in the following form:

We define ...

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