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...
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...
In this work, we investigate the Perfectly Matched Layers (PML) introduced by Bérenger [3] for designing efficient numerical absorbing layers in electromagnetism. We make a mathematical analysis of this model, first via a modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This last...
In this article, we derive a complete mathematical analysis of a
coupled 1D-2D model for 2D wave propagation in media including thin
slots. Our error estimates are illustrated by numerical results.
We are concerned with a 2D time harmonic wave propagation
problem in a medium including a thin slot whose thickness
is small with respect to the wavelength. In a previous article, we derived
formally an asymptotic expansion of the solution with respect to
using the method of matched asymptotic expansions. We also proved the
existence and uniqueness of the terms of the asymptotics. In this paper,
we complete the mathematical justification of our work by deriving optimal error estimates between...
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...
In this paper we are interested in the numerical modeling
of absorbing ferromagnetic materials
obeying the non-linear Landau-Lifchitz-Gilbert law with respect to the
propagation and scattering of electromagnetic waves.
In this work
we consider the 1D problem.
We first show that the corresponding Cauchy problem
has a unique global solution.
We then derive a numerical scheme based on an appropriate modification
of Yee's scheme, that we show to preserve some important
properties of the continuous...
In this work, we investigate the Perfectly
Matched Layers (PML)
introduced by Bérenger [3] for designing
efficient numerical absorbing
layers in electromagnetism.
We make a mathematical analysis of this model, first a modal
analysis with standard Fourier techniques, then energy
techniques. We obtain uniform in time stability results (that make
precise some results known in the literature) and state some energy
decay results that illustrate the absorbing properties of the
model. This last technique...
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