Homogenization for transient waves in 1D periodic media: dispersion, interfaces and point sources
Résumé
In the context of linear waves in 1D microstructured media, an homogenized model is proposed. It combines second-order asymptotic homogenization to account for dispersion, a reformulation into an hyperbolic system, and interface correctors to model transmssion from or towards homogeneous media. The well posedness of this "total model" is proven and its efficiency is illustrated via numerical simulations. An extension to Dirac source terms is proposed.
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