Bengt Fornberg (Colorado. USA)

Some numerical techniques for Maxwell's equations in different types of geometries

Abstract

Almost all the difficulties that arise in the numerical solution of Maxwell's equations are due to material interfaces (to which we include objects, such as antenna wires, etc.) Very 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 discretization, 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 latter 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. We will here discuss that method - known as ADI-FDTD - and also several subsequent further developments in this area.