Remarks on the stability of Cartesian PMLs in corners

TL;DR

This paper investigates the stability of Cartesian PMLs in corners for hyperbolic systems, analyzing both continuous and discrete cases, and demonstrates how discretization choices affect stability through theoretical and numerical results.

Contribution

It provides new stability results for Cartesian PMLs in corners at both continuous and discrete levels, including a spectral finite element discretization and analysis of time discretization effects.

Findings

Stability results for Cartesian PMLs in corners at continuous level.

Discretization choices impact CFL stability conditions.

Numerical illustrations confirm theoretical stability analysis.

Abstract

This work is a contribution to the understanding of the question of stability of Perfectly Matched Layers (PMLs) in corners, at continuous and discrete levels. First, stability results are presented for the Cartesian PMLs associated to a general first-order hyperbolic system. Then, in the context of the pressure-velocity formulation of the acoustic wave propagation, an unsplit PML formulation is discretized with spectral mixed finite elements in space and finite differences in time. It is shown, through the stability analysis of two different schemes, how a bad choice of the time discretization can deteriorate the CFL stability condition. Some numerical results are finally presented to illustrate these stability results.