## 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 inuence 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.

Original language | English (US) |
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Pages (from-to) | 423-455 |

Number of pages | 33 |

Journal | ESAIM: Mathematical Modelling and Numerical Analysis |

Volume | 52 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1 2018 |

Externally published | Yes |

## Keywords

- Coupling of finite and boundary elements
- Groups of isometries
- Piezoelectricity
- Retarded potentials
- Time-domain boundary integral equations
- Wave-structure interaction

## ASJC Scopus subject areas

- Analysis
- Numerical Analysis
- Modeling and Simulation
- Computational Mathematics
- Applied Mathematics