Introduction to Perfectly Matched Layers
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.
Bérenger’s PML formulation is usually referred to as the split PML, because the unknowns are split into a sum of nonphysical components in PML domains. Another formulation that does not require splitting the variables is based on the coordinate transformation in PML domains, where the real coordinate is mapped onto the complex plane:
(2-57).
For example, the mapping Equation 2-57 will transform the 1D Helmholtz equation as follows:
(2-58).
Infinite Elements, Perfectly Matched Layers, and Absorbing Layers in the COMSOL Multiphysics Reference Manual