The concept of a perfectly matched layer (PML) as an absorbing boundary condition was introduced by Bérenger (Ref. 38) with regard to the system of Maxwell’s equations. The PML provided absorption of propagating waves without introducing reflections from the interface between the PML and the physical domain. This made the PML technique attractive for treating open domain problems for acoustic, elastic, and electromagnetic wave propagation.
For example, the mapping Equation 2-53 will transform the 1D Helmholtz equation as follows: