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Symmetric Boundary-Finite Element Discretization of Time Dependent Acoustic Scattering by Elastic Obstacles with Piezoelectric Behavior

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Abstract

A coupled BEM/FEM formulation for the transient interaction between an acoustic field and a piezoelectric scatterer is proposed. The scattered part of the acoustic wave is represented in terms of retarded layer potentials while the elastic displacement and electric potential are treated variationally. This results in an integro-differential system. Well posedness of a general Galerkin semi-discretization in space of the problem is shown in the Laplace domain and translated into explicit stability bounds in the time domain. Trapezoidal-rule and BDF2 convolution quadrature are used in combination with matching time stepping for time discretization. Second order convergence is proven for the BDF2-based method. Numerical experiments are provided for BDF2 and trapezoidal rule based time evolution.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Delaware, Newark, DE, USA

    Tonatiuh Sánchez-Vizuet & Francisco-Javier Sayas

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  1. Tonatiuh Sánchez-Vizuet
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  2. Francisco-Javier Sayas
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Correspondence to Francisco-Javier Sayas.

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TSV and FJS partially funded by NSF Grant DMS 1216356.

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Sánchez-Vizuet, T., Sayas, FJ. Symmetric Boundary-Finite Element Discretization of Time Dependent Acoustic Scattering by Elastic Obstacles with Piezoelectric Behavior. J Sci Comput 70, 1290–1315 (2017). https://doi.org/10.1007/s10915-016-0281-y

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  • DOI: https://doi.org/10.1007/s10915-016-0281-y

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