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Stability and Convergence Analysis of Time-domain Perfectly Matched Layers for The Wave Equation in Waveguides

Eliane Bécache 1 Maryna Kachanovska 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : This work is dedicated to the proof of stability and convergence of the Bérenger's perfectly matched layers in the waveguides for an arbitrary L ∞ damping function. The proof relies on the Laplace domain techniques and an explicit representation of the solution to the PML problem in the waveguide. A bound for the PML error that depends on the absorption parameter and the length of the PML is presented. Numerical experiments confirm the theoretical findings.
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Submitted on : Wednesday, April 8, 2020 - 9:56:45 AM
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Eliane Bécache, Maryna Kachanovska. Stability and Convergence Analysis of Time-domain Perfectly Matched Layers for The Wave Equation in Waveguides. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2021, ⟨10.1137/20M1330543⟩. ⟨hal-02536375⟩

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