An exact bounded perfectly matched layer for time-harmonic scattering problems

The aim of this paper is to introduce an exact bounded perfectly matched layer (PML) for the scalar Helmholtz equation. This PML is based on using a nonintegrable absorbing function. Exactness must be understood in the sense that this technique allows exact recovering of the solution to time-harmonic scattering problems in unbounded domains. In spite of the singularity of the absorbing function, the coupled fluid/PML problem is well posed when the solution is sought in an adequate weighted Sobolev space. The resulting weak formulation can be numerically solved by using standard finite elements. The high accuracy of this approach is numerically demonstrated as compared with a classical PML technique.