A perfectly matched layer for the Helmholtz equation in a semi-infinite strip

The perfectly matched layer (PML) has become a widespread technique for preventing reflections from far field boundaries for wave propagation problems in both the time dependent and frequency domains. We develop a discretization to solve the Helmholtz equation in an infinite two-dimensional strip. We solve the interior equation using high-order finite differences schemes. The combined Helmholtz-PML problem is then analyzed for the parameters that give the best performance. We show that the use of local high-order methods in the physical domain coupled with a specific second order approximation in the PML yields global high-order accuracy in the physical domain. We discuss the impact of the parameters on the effectiveness of the PML. Numerical results are presented to support the analysis.