Optimizing the PML in the discrete context

Perfectly Matched Layers (PML) are widely used for the simulation of unbounded wave-like problems. However their performance depends critically on both an absorption coefficient and the spatial discretization. Tuning the coefficient requires a costly (and case-dependent) optimization procedures... so that in most applications it is set empirically.

In this talk we discuss the influence of the absorption coefficient on the PML performance for time-domain simulations, in both continuous and discrete contexts. We present efficient coefficients that allow to avoid any tuning in discrete contexts, and compare those with other frequent choices by means of benchmarks solved with both finite differences and finite elements (continuous and discontinuous). A realistic 3D discontinuous Galerkin benchmark for Maxwell's equations will highlight the advantages of our approach.