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On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations. (English) Zbl 0992.78032

We investigate the Perfectly Matched Layers (PML) introduced by Bérenger for designing efficient numerical absorbing layers in electromagnetism. We make a mathematical analysis of this model, first via a modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This last technique allows us to prove the stability of the Yee’s scheme for discretizing PML’s.

MSC:

78M20 Finite difference methods applied to problems in optics and electromagnetic theory
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L40 First-order hyperbolic systems
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References:

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