Abstract
Almost all the difficulties that arise in finite difference time domain solutions of Maxwell's equations are due to material interfaces (to which we include objects such as antennas, wires, etc.) Different types of difficulties arise if the geometrical features are much larger than or much smaller than a typical wave length. In the former case, the main difficulty has to do with the spatial discretisation, which needs to combine good geometrical flexibility with a relatively high order of accuracy. After discussing some options for this situation, we focus on the tatter case. The main problem here is to find a time stepping method which combines a very low cost per time step with unconditional stability. The first such method was introduced in 1999 and is based on the ADI principle. We will here discuss that method and some subsequent developments in this area.
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