Evolution of a semidiscrete system modeling the scattering of acoustic waves by a piezoelectric solid

Abstract

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.

References in corpus (4)

• Boundary and coupled boundary-finite element methods for transient wave-structure interaction
• A fully discrete BEM-FEM scheme for transient acoustic waves
• A new and improved analysis of the time domain boundary integral operators for acoustics
• Boundary-Finite Element discretization of time dependent acoustic scattering by elastic obstacles with piezoelectric behavior

Cited by in corpus (4)

• Time-Domain Boundary Integral Methods in Linear Thermoelasticity
• Time-Dependent Wave-Structure Interaction Revisited: Thermo-piezoelectric Scatterers
• Time domain boundary integral equations and convolution quadrature for scattering by composite media (extended preprint)
• A boundary integral equation formulation for transient electromagnetic transmission problems on Lipschitz domains