Some unconditionally stable time stepping methods for the 3D Maxwellʹs equations

Almost all the difficulties that arise in the numerical solution of Maxwellʹs 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.