A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Three-dimensional perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer
Journal of Computational Physics
A mathematical analysis of the PML method
Journal of Computational Physics
On the analysis and construction of perfectly matched layers for the linearized Euler equations
Journal of Computational Physics
On the construction and analysis of absorbing layers in CEM
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Numerical solution of problems on unbounded domains. a review
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Long-time numerical computation of wave-type solutions driven by moving sources
Applied Numerical Mathematics
Global discrete artificial boundary conditions for time-dependent wave propagation
Journal of Computational Physics
Long Time Behavior of the Perfectly Matched Layer Equations in Computational Electromagnetics
Journal of Scientific Computing
Artificial boundary conditions for the numerical simulation of unsteady acoustic waves
Journal of Computational Physics
On the application of lacunae-based methods to Maxwell's equations
Journal of Computational Physics
Non-Linear PML Equations for Time Dependent Electromagnetics in Three Dimensions
Journal of Scientific Computing
Long-Time Performance of Unsplit PMLs with Explicit Second Order Schemes
Journal of Scientific Computing
Long-Time Performance of Unsplit PMLs with Explicit Second Order Schemes
Journal of Scientific Computing
Journal of Computational Physics
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Perfectly matched layers (PMLs) are used for the numerical solution of wave propagation problems on unbounded regions. They surround the finite computational domain (obtained by truncation) and are designed to attenuate and completely absorb all the outgoing waves while producing no reflections from the interface between the domain and the layer. PMLs have demonstrated excellent performance for many applications. However, they have also been found prone to instabilities that manifest themselves when the simulation time is long. Hereafter, we propose a modification that stabilizes any PML applied to a hyperbolic partial differential equation/system that satisfies the Huygens' principle (such as the 3D d'Alembert equation or Maxwell's equations in vacuum). The modification makes use of the presence of lacunae in the corresponding solutions and allows us to establish a temporally uniform error bound for arbitrarily long-time intervals. At the same time, it does not change the original PML equations. Hence, the matching properties of the layer, as well as any other properties deemed important, are fully preserved. We also emphasize that besides the aforementioned PML instabilities per se, the methodology can be used to cure any other undesirable long-term computational phenomenon, such as the accuracy loss of low order absorbing boundary conditions.