The effective modeling of wave propagation problems on unbounded domains by numerical techniques, such as the finite difference or the finite element method, is dependent on the particular absorbing boundary condition used to truncate the computational domain. In 1994, J. P. Berenger created the perfectly matched layer (PML) technique for the reflectionless absorption of electromagnetic waves in the time domain. The PML is an absorbing layer that is placed around the computational domain of interest in order to attenuate outgoing radiation. Berenger showed that his continuous PML model allowed perfect transmission of electromagnetic waves across the interface of the computational domain regardless of the frequency, polarization or angle of incidence of the waves. The waves are then attenuated exponentially with respect to depth into the absorbing layers.
In this talk, we will describe the original (split field) PML technique of Berenger as well as some modified PML models. We will then discuss some recent work that analyzes the Uniaxial Perfectly matched layer (UPML) model applied to Maxwell's equations in linear dispersive media using energy techniques. Uniform in time stability results are obtained under certain assumptions on the UPML parameters. We also obtain some energy decay results under additional assumptions on the UPML parameters. Lastly, the implementation of the PML using mixed finite element methods will be considered, along with stability of the resulting numerical method.