The aim of this talk is to introduce an 'exact' bounded perfectly
matched layer (PML) for the scalar Helmholtz equation. This PML is
based on using a singular damping function in the complex-valued
coordinate stretching. '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 damping function, the procedure leads to a well posed conforming
finite element discretization. The high accuracy of this approach is
numerically demonstrated, as well as its efficiency as compared with
classical PML techniques.