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: email@example.com
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.