Abstract
Almost all the difficulties that arise in the numerical solution of Maxwell's equations are due to material interfaces. In case that their geometrical features are much smaller than a typical wavelength, one would like to use small space steps with large time steps. The first time stepping method which combines a very low cost per time step with unconditional stability was the ADI-FDTD method introduced in 1999. The present discussion starts with this method, and with an even more recent Crank–Nicolson-based split step method with similar properties. We then explore how these methods can be made even more efficient by combining them with techniques that increase their temporal accuracies.
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