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- Title
ANALYSIS OF AN INTERACTION PROBLEM BETWEEN AN ELECTROMAGNETIC FIELD AND AN ELASTIC BODY.
- Authors
Bernardo, Antonio; Márquez, Antonio; Meddahi, Salim
- Abstract
This paper deals with an interaction problem between a solid and an electromagnetic field in the frequency domain. More precisely, we aim to compute both the magnetic component of the scattered wave and the elastic vibrations that take place in the solid elastic body. To this end, we solve a transmission problem holding between the bounded domain Ωs ⊂ ℝ3 representing the obstacle and a sufficiently large annular region surrounding it. We point out here that (following Voigt's model, cf. [12]) we only allow the electromagnetic field to interact with the elastic body through the boundary of s. We apply the abstract framework developed in the work [3] by A. Buffa to prove that our coupled variational formulation is well posed. We define the corresponding discrete scheme by using the edge element in the electromagnetic domain and standard Lagrange finite elements in the solid domain. Then we show that the resulting Galerkin scheme is uniquely solvable, convergent and we derive optimal error estimates. Finally, we illustrate our analysis with some results from computational experiments.
- Subjects
ELECTROMAGNETIC fields; ELASTIC analysis (Engineering); VOIGT effect; VOIGT reaction; SCATTERING (Mathematics); LAGRANGE problem; NUMERICAL solutions to Lagrange equations; GALERKIN methods; FINITE element method
- Publication
International Journal of Numerical Analysis & Modeling, 2010, Vol 7, Issue 4, p749
- ISSN
1705-5105
- Publication type
Article