# Mathematical and numerical modelling of piezoelectric sensors

Sebastien Imperiale; Patrick Joly

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

- Volume: 46, Issue: 4, page 875-909
- ISSN: 0764-583X

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topImperiale, Sebastien, and Joly, Patrick. "Mathematical and numerical modelling of piezoelectric sensors." ESAIM: Mathematical Modelling and Numerical Analysis 46.4 (2012): 875-909. <http://eudml.org/doc/277852>.

@article{Imperiale2012,

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.},

author = {Imperiale, Sebastien, Joly, Patrick},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Piezoelectricity; quasi-static approximation; ultrasonic sensors; piezoelectricity; quasi-state approximation; ultrasonic sensor},

language = {eng},

month = {2},

number = {4},

pages = {875-909},

publisher = {EDP Sciences},

title = {Mathematical and numerical modelling of piezoelectric sensors},

url = {http://eudml.org/doc/277852},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Imperiale, Sebastien

AU - Joly, Patrick

TI - Mathematical and numerical modelling of piezoelectric sensors

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2012/2//

PB - EDP Sciences

VL - 46

IS - 4

SP - 875

EP - 909

AB - 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.

LA - eng

KW - Piezoelectricity; quasi-static approximation; ultrasonic sensors; piezoelectricity; quasi-state approximation; ultrasonic sensor

UR - http://eudml.org/doc/277852

ER -

## References

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