Analytic time-domain performance analysis of absorbing boundary conditions and perfectly matched layers

Transient wave propagation and scattering problems are often analyzed in configurations of unbounded extent. To bound the domain in a computational algorithm, boundary conditions are employed such that the field values in its interior are not disturbed with respect to some error criterion. The performance of these so-called absorbing boundary conditions is usually tested by purely numerical means. The present contribution investigates the performance of a number of absorbing boundary conditions in a test configuration where analytic time-domain expressions for the field quantities are known. Also, we include in the analysis the performance of a truncated perfectly matched layer.