PML Condition for the Numerical Simulation of Acoustic Wave

In the numerical simulation of the wave equation, to develop an absorbing boundary condition in the finite domain is a very important problem. Berenger introduced a new condition called the perfectly matched layer, which has the remarkable property of having a zero reflection. Over the last decades, the PML has been used in the context of the acoustic wave equation formulated as a first-order system in velocity and stress, but hasn´t been used in the context of numerical schemes that are based on the wave equation written as a second-order system in displacement. The goal of this article is to reformulate PML condition in order to use it in this context.