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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2012

Mathematical and numerical modelling of piezoelectric sensors

Abstract

The present work aims at proposing a rigorous analysis of the mathematical and numerical modelling of ultrasonic piezoelectric sensors. This includes the well-posedness of the final model, the rigorous justification of the underlying approximation and the design and analysis of numerical methods. More precisely, we first justify mathematically the classical quasi-static approximation that reduces the electric unknowns to a scalar electric potential. We next justify the reduction of the computation of this electric potential to the piezoelectric domains only. Particular attention is devoted to the different boundary conditions used to model the emission and reception regimes of the sensor. Finally, an energy preserving finite element / finite difference numerical scheme is developed; its stability is analyzed and numerical results are presented.
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Dates and versions

hal-00869631 , version 1 (03-10-2013)

Identifiers

  • HAL Id : hal-00869631 , version 1

Cite

Sébastien Imperiale, Patrick Joly. Mathematical and numerical modelling of piezoelectric sensors. ESAIM: Mathematical Modelling and Numerical Analysis, 2012. ⟨hal-00869631⟩
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