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Guided elastic waves and perfectly matched layers. (English) Zbl 1231.74188
Summary: Elastic waveguides support propagating modes that have two possible features, negative group velocities and long wavelengths that, for some frequencies, degrade the accuracy or otherwise poison existing numerical schemes that utilise perfectly matched layers (PMLs) to mimic infinite domains. We illustrate why negative group velocities and long waves are potentially an issue and describe how these problems are overcome. Detailed numerical simulations confirm the accuracy of the modified scheme and provide both theoretical and pragmatic estimates for the parameters within the PML model, in particular for the damping function. We also contrast and compare different implementations of the PML model using spectral and finite difference methods.

MSC:
74J05 Linear waves in solid mechanics
74S20 Finite difference methods applied to problems in solid mechanics
74S25 Spectral and related methods applied to problems in solid mechanics
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
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