An optimal perfectly matched layer with unbounded absorbing function for time-harmonic acoustic scattering problems

We introduce an optimal bounded perfectly matched layer (PML) technique by choosing a particular absorbing function with unbounded integral. With this choice, spurious reflections are avoided, even though the thickness of the layer is finite. We show that such choice is easy to implement in a finite element method and overcomes the dependency of parameters for the discrete problem. Finally, its efficiency and accuracy are illustrated with some numerical tests.