Mathematical Analysis of a Perfectly Matched Layer Model and Finite Element Simulations

The Perfectly Matched Layers (PML) technique proposed by Bérenger in 1994 is a powerful tool in computational electromagnetics and wave simulation on unbounded domains. A good PML model can be used to truncate infinite open-space computational domains into finite, manageable grids with virtually zero artificial reflection. Since 1994, there are many PML models proposed and performed very well in practice for Maxwell’s equations, rigorous mathematical analysis of many PML models are still missing. In this paper, we successfully established the stability results for a PML model implemented in [23]. Corresponding finite element schemes are proposed and implemented to demonstrate the wave absorbing capability of this PML model in two different forms.