Absorbing boundary conditions and perfectly matched layers - an analytic time-domain performance analysis

The time-domain performance of a number of absorbing boundary conditions invoked on the boundary of a domain of computation, as well as of a perfectly matched layer surrounding such a domain, is carried out for a test configuration for which analytic expressions for the relevant field quantities exist. The test configuration consists of a small loop antenna radiating into a homogeneous, isotropic half-space. On the planar boundary of this halfspace, either an absorbing boundary condition is invoked or a perfectly matched layer is started that is truncated at some finite depth of penetration. For a loop parallel to the boundary, closed-form analytic expressions for all field components of the spuriously reflected field are presented for all truncation conditions involved. A number of important features show up that might be masked in purely numerical implementations of the procedures under consideration.