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.
Accepté le :
DOI : 10.1051/m2an/2017045
Mots clés : Piezoelectricity, coupling of finite and boundary elements, retarded potentials, wave-structure interaction, time-domain boundary integral equations, groups of isometries
@article{M2AN_2018__52_2_423_0,
author = {Brown, Thomas S. and S\'anchez-Vizuet, Tonatiuh and Sayas, Francisco-Javier},
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},
number = {2},
year = {2018},
doi = {10.1051/m2an/2017045},
zbl = {06966729},
mrnumber = {3834431},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2017045/}
}
TY - JOUR AU - Brown, Thomas S. AU - Sánchez-Vizuet, Tonatiuh AU - Sayas, Francisco-Javier TI - Evolution of a semidiscrete system modeling the scattering of acoustic waves by a piezoelectric solid JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 423 EP - 455 VL - 52 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2017045/ DO - 10.1051/m2an/2017045 LA - en ID - M2AN_2018__52_2_423_0 ER -
%0 Journal Article %A Brown, Thomas S. %A Sánchez-Vizuet, Tonatiuh %A Sayas, Francisco-Javier %T Evolution of a semidiscrete system modeling the scattering of acoustic waves by a piezoelectric solid %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 423-455 %V 52 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2017045/ %R 10.1051/m2an/2017045 %G en %F M2AN_2018__52_2_423_0
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. http://www.numdam.org/articles/10.1051/m2an/2017045/
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