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    Two-dimensional wave propagation in layered periodic media

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    1309.6666v2.pdf
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    Type
    Article
    Authors
    Quezada de Luna, Manuel
    Ketcheson, David I. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Numerical Mathematics Group
    Date
    2014-12-03
    Online Publication Date
    2014-12-03
    Print Publication Date
    2014-01
    Permanent link to this record
    http://hdl.handle.net/10754/333681
    
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    Abstract
    We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with constant impedance exhibit no effective dispersion. We show that a new kind of effective dispersion may arise in two dimensions, even in materials with constant impedance. This dispersion is a macroscopic effect of microscopic diffraction caused by spatial variation in the sound speed. We analyze this dispersive effect by using highorder homogenization to derive an anisotropic, dispersive effective medium. We generalize to two dimensions a homogenization approach that has been used previously for one-dimensional problems. Pseudospectral solutions of the effective medium equations agree to high accuracy with finite volume direct numerical simulations of the variable-coeffi cient equations.
    Citation
    Quezada de Luna, M., & Ketcheson, D. I. (2014). Two-Dimensional Wave Propagation in Layered Periodic Media. SIAM Journal on Applied Mathematics, 74(6), 1852–1869. doi:10.1137/130937962
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Journal on Applied Mathematics
    DOI
    10.1137/130937962
    arXiv
    1309.6666
    Additional Links
    http://arxiv.org/abs/1309.6666
    https://github.com/ketch/effective_dispersion_RR
    ae974a485f413a2113503eed53cd6c53
    10.1137/130937962
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Numerical Mathematics Group; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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