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Numerical modeling and investigations of 3D devices with ferroelectric layer fully embedded in a paraelectric environment. (English) Zbl 1419.82073

Summary: We investigate three-dimensional devices made up of a ferroelectric layer that is fully embedded in a paraelectric environment, by modeling based on the Ginzburg-Landau formalism as well as on the Electrostatics equations, and boundary conditions that are suitable for applications. From finite element approximations and inexact Newton techniques for solving numerically the resulting nonlinear system, we develop two numerical protocols. The first protocol concerns a determination of states related to the system and incorporates a process of heating as well as of cooling of devices, in terms of the temperature, whereas the second one is devoted to the existence study of hysteresis loops. The efficiency of these protocols is particularly emphasized from numerical simulations.

MSC:

82D45 Statistical mechanics of ferroelectrics
82D80 Statistical mechanics of nanostructures and nanoparticles
35Q56 Ginzburg-Landau equations
47H10 Fixed-point theorems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
49M15 Newton-type methods
78A30 Electro- and magnetostatics
65H10 Numerical computation of solutions to systems of equations
65F10 Iterative numerical methods for linear systems
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References:

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