The use of lacunas of hyperbolic equations and the difference potential method for computing wave diffraction in a bounded neighborhood of a scatterer at long times

Artificial boundary conditions that are equivalent to a difference analogue of the Maxwell system in a vacuum outside the computational subdomain are constructed, and an algorithm for calculating them is developed. The computational cost of this algorithm per time step is proportional to the number of points in the computational subdomain and is independent of the step number. The approach combines the use of lacunas with the difference potential method. A brief review of earlier results based on this approach is presented.