Mathematical and numerical modelling of piezoelectric sensors
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 4, pp. 875-909.

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.

DOI : 10.1051/m2an/2011070
Classification : 35L05, 35A35, 73R05, 35A40
Mots-clés : piezoelectricity, quasi-static approximation, ultrasonic sensors 
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Imperiale, Sebastien; Joly, Patrick. Mathematical and numerical modelling of piezoelectric sensors. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 4, pp. 875-909. doi : 10.1051/m2an/2011070. http://www.numdam.org/articles/10.1051/m2an/2011070/

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