  For numerical simulations of highly relativistic and transversely accelerated
charged particles including radiation fast algorithms are needed. While the
radiation in particle accelerators has wavelengths in the order of 100 um the
computational domain has dimensions roughly 5 orders of magnitude larger
resulting in very large mesh sizes. The particles are confined to a small area
of this domain only. To resolve the smallest scales close to the particles
subgrids are envisioned. For reasons of stability the alternating direction
implicit (ADI) scheme by D. N. Smithe et al. (J. Comput. Phys. 228 (2009)
pp.7289-7299) for Maxwell equations has been adopted. At the boundary of the
domain absorbing boundary conditions have to be employed to prevent reflection
of the radiation. In this paper we show how the divergence preserving ADI
scheme has to be formulated in perfectly matched layers (PML) and compare the
performance in several scenarios.
