Evolution of a semidiscrete system modeling the scattering of acoustic waves by a piezoelectric solid
| Autor: | Thomas S. Brown, Tonatiuh Sánchez-Vizuet, Francisco-Javier Sayas |
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| Rok vydání: | 2018 |
| Předmět: |
Physics
Numerical Analysis Discretization 65J08 65M38 65M60 65R20 Cauchy stress tensor Applied Mathematics Operator (physics) Mathematical analysis Numerical Analysis (math.NA) 010103 numerical & computational mathematics Acoustic wave 01 natural sciences Finite element method 010101 applied mathematics Computational Mathematics Modeling and Simulation Electric field FOS: Mathematics Mathematics - Numerical Analysis 0101 mathematics Boundary element method Electric displacement field Analysis |
| Zdroj: | ESAIM: Mathematical Modelling and Numerical Analysis. 52:423-455 |
| ISSN: | 1290-3841 0764-583X |
| DOI: | 10.1051/m2an/2017045 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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