Numerical Analysis of the Electro-Magnetic Perfectly Matched Layer in a Discontinuous Galerkin Discretization

This work is devoted to the numerical analysis of time-domain linear Maxwell's equations in a discontinuous Galerkin discretization. We focus on Berenger's perfectly matched layer and have a detailed look at construction, well-posedness, and semi-discrete error analysis. We present an analytic solution to the system, that can be utilized to efficiently determine optimal parameter values for the layer and state a way to avoid an exponential growth in time of the semi-discrete error bound.