Matched Layers, Perfect and Otherwise

Some twenty years ago Berenger introduced the remarkable method of perfectly matched layers for truncating to a rectangle, the computation of solutions of Maxwell's equations in 1+2 and 1+3 dimensional space time. Only recently have some of the fundamental questions concerning this method been resolved. For example the stability of the original method and its perfection. We discuss the analysis of this and related methods that are constructed to perform better in variable coefficient settings where the perfection of Berenger no longer holds. Research done with Laurence Haplern, Sabrina Petit, and Ludovic Métivier.