Geodesic
Evolution of a semidiscrete system modeling the scattering of acoustic waves by a piezoelectric solid
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 2, pp. 423-455

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We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing electric field. The system is closed using Gauss’s law for the associated electric displacement. Well-posedness of the system is studied by its reformulation as a first order in space and time differential system with help of an elliptic lifting operator. We then proceed to studying a semidiscrete formulation, corresponding to an abstract Finite Element discretization in the electric and elastic fields, combined with an abstract Boundary Element approximation of a retarded potential representation of the acoustic field. The results obtained with this approach improve estimates obtained with Laplace domain techniques. While numerical experiments illustrating convergence of a fully discrete version of this problem had already been published, we demonstrate some properties of the full model with some simulations for the two dimensional case.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2017045
Classification : 65J08, 65M38, 65M60, 65R20
Keywords: Piezoelectricity, coupling of finite and boundary elements, retarded potentials, wave-structure interaction, time-domain boundary integral equations, groups of isometries

Brown, Thomas S. 1 ; Sánchez-Vizuet, Tonatiuh 1 ; Sayas, Francisco-Javier 1

1 
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     title = {Evolution of a semidiscrete system modeling the scattering of acoustic waves by a piezoelectric solid},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {423--455},
     publisher = {EDP-Sciences},
     volume = {52},
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     doi = {10.1051/m2an/2017045},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017045/}
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Brown, Thomas S.; Sánchez-Vizuet, Tonatiuh; Sayas, Francisco-Javier. Evolution of a semidiscrete system modeling the scattering of acoustic waves by a piezoelectric solid. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 2, pp. 423-455. doi: 10.1051/m2an/2017045

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