Manuel Sánchez

Pontificia Universidad Católica de Chile, Chile 

We propose discrete-analytic Perfectly Matched Layers (PMLs) for high-order finite difference (FD) discretizations of the scalar wave equation which, unlike PDE-based PMLs, produce no numerical reflections (up to machine precision) at the PML interface. Our approach generalizes the ideas put forth in a recent paper [Journal of Computational Physics 381 (2019)] for the standard second-order FD method,  to arbitrary high-order schemes at the cost of introducing additional localized PML variables that account for the larger stencils used. We prove that the numerical solutions produced by the proposed schemes decay exponentially fast as they propagate within the PML domain. The merits of the method are demonstrated in a variety of numerical examples including waveguide problems where high-order schemes are often needed to mitigate undesired numerical dispersion errors