Perfectly matched layers in time domain. A simple two-dimensional error analysis

Abstract: Perfectly Matched Layers (PML) has become a very common method for the numerical approximation of wave and wave-like equations on unbounded domains. This technique allows one to obtain accurate solutions while working on a finite computational domain, and the technique is relatively simple to implement. Results concerning the accuracy of the PML method have been obtained, but mostly with regard problems at a fixed frequency. In this paper we provide very explicit time-domain bounds on the accuracy of PML for the two-dimensional wave equation and illustrate our conclusions with some numerical examples.