Analysis of the PML equations in general convex geometry

In this work, we study a mesh termination scheme in acoustic scattering, kn own as the perfectly matched layer (PML) method. The main result of the pap er is the following. Assume that the scatterer is contained in a bounded an d strictly convex artificial domain. We surround this domain by a PML of co nstant thickness. On the peripheral boundary of this layer, a homogenous Di richlet condition is imposed. We show in this paper that the resulting boun dary-value problem for the scattered field is uniquely solvable for all wav enumbers and the solution within the artificial domain converges exponentia lly fast toward the full-space scattering solution when the layer thickness is increased. The proof is based on the idea of interpreting the PML mediu m as a complex stretching of the coordinates in R-n and on the use of compl exified layer potential techniques.