Evolution of a semidiscrete system modeling the scattering of acoustic waves by a piezoelectric solid
Provides rigorous analysis for a coupled FEM-BEM method in piezoelectric scattering, improving on previous Laplace-domain estimates, but the contribution is incremental for the specialized domain of computational acoustics.
The paper proves well-posedness and improved stability estimates for a semidiscrete model coupling finite elements (elastic/electric fields) with boundary elements (acoustic field) for acoustic wave scattering by a piezoelectric solid. Numerical simulations in 2D demonstrate model properties.
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.