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

appa-image147-02.gif

For normalized field values, we obtain:

appa-image148-01.gif

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

appa-image148-02.gif

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:

appa-image149-02.gif

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:

appa-image149-03.gif

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

We define ...

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