Volume 52, Number 2, March–April 2018
|Page(s)||423 - 455|
|Published online||31 May 2018|
Evolution of a semidiscrete system modeling the scattering of acoustic waves by a piezoelectric solid
Department of Mathematical Sciences, University of Delaware,
2 Courant Institute of Mathematical Sciences, New York University, New York, USA
* Corresponding author: firstname.lastname@example.org
Accepted: 27 August 2017
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.
Mathematics Subject Classification: 65J08 / 65M38 / 65M60 / 65R20
Key words: Piezoelectricity / coupling of finite and boundary elements / retarded potentials / wave-structure interaction / time-domain boundary integral equations / groups of isometries
© EDP Sciences, SMAI 2018
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