Displaying similar documents to “Mathematical and numerical modelling of piezoelectric sensors”

Mathematical and numerical modelling of piezoelectric sensors

Sebastien Imperiale, Patrick Joly (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

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...

Mathematical and numerical modelling of piezoelectric sensors

Sebastien Imperiale, Patrick Joly (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

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...

Numerical approximation of nematic liquid crystal flows governed by the Ericksen-Leslie equations

Noel J. Walkington (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Numerical approximation of the flow of liquid crystals governed by the Ericksen-Leslie equations is considered. Care is taken to develop numerical schemes which inherit the Hamiltonian structure of these equations and associated stability properties. For a large class of material parameters compactness of the discrete solutions is established which guarantees convergence.

On the Numerical Modeling of Deformations of Pressurized Martensitic Thin Films

Pavel Bělík, Timothy Brule, Mitchell Luskin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We propose, analyze, and compare several numerical methods for the computation of the deformation of a pressurized martensitic thin film. Numerical results have been obtained for the hysteresis of the deformation as the film transforms reversibly from austenite to martensite.

Non-local damage modelling of quasi-brittle composites

Jiří Vala, Vladislav Kozák (2021)

Applications of Mathematics

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Most building materials can be characterized as quasi-brittle composites with a cementitious matrix, reinforced by some stiffening particles or elements. Their massive exploitation motivates the development of numerical modelling and simulation of behaviour of such material class under mechanical, thermal, etc. loads, including the evaluation of the risk of initiation and development of micro- and macro-fracture. This paper demonstrates the possibility of certain deterministic prediction,...

Reliable numerical modelling of malaria propagation

István Faragó, Miklós Emil Mincsovics, Rahele Mosleh (2018)

Applications of Mathematics

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We investigate biological processes, particularly the propagation of malaria. Both the continuous and the numerical models on some fixed mesh should preserve the basic qualitative properties of the original phenomenon. Our main goal is to give the conditions for the discrete (numerical) models of the malaria phenomena under which they possess some given qualitative property, namely, to be between zero and one. The conditions which guarantee this requirement are related to the time-discretization...