A preconditioner for the Helmholtz equation with perfectly matched layer

This paper discusses an iterative method for solving the Helmholtz equation with the perfectly matched layer (PML). The method consists of an outer and inner iteration process. The inner iteration is used to approximately solve a preconditioner, which in this case is based on a modified PML equation. The outer iteration is a Krylov subspace method (Bi-CGSTAB). The method explained here is identical with the method already discussed and proposed, e.g., in [Erlangga, Oosterlee, Vuik, SIAM J. Sci. Comput., 27 (2006), pp. 1471-1492]. We show that the extension of the method to the PML equation is straight-forward, and the performance for this type of problem does not degrade as compared to Helmholtz problems with, e.g. Engquist and Majda's second order boundary condition