# Author Archives: Sébastien Imperiale

## (Closed) PhD position

A PhD position is open in the team. The objective of the PhD is to develop a rigorous mathematical and numerical background for the extension and dissemination of imaging modalities by ultrasound, i.e., elastic waves, applied to the cardiac settings. The problems treated will concerned the topics of mathematical modelling, Continue Reading(Closed) PhD position

## Mathematical and numerical modelling of coaxial cables

Derivation and justification of a generalised telegraphist’s model for coaxial cables In this work, we focus on the time-domain simulation of the propagation of electromagnetic waves in non-homogeneous lossy coaxial cables. The full 3D Maxwell equations, that described the propagation of current and electric potential in such cables, are classically Continue ReadingMathematical and numerical modelling of coaxial cables

## Wave-based inverse problems

Transient elastography The approach studied here is to be linked to the so-called hybrid inverse problems. Having been made available internally as the solution of a preliminary wave based inverse problem, the full-field measurements considered are used to construct by local algebraic manipulations a system, possibly redundant, of PDE whose Continue ReadingWave-based inverse problems

## Efficient time discretization for wave equations

High order theta schemes for the wave equation High order theta schemes are new time discretisation schemes for the wave equation based upon the modified equation technique and the implicit theta scheme. In the context of a (high order) finite element discretization in space of a wave equation the following Continue ReadingEfficient time discretization for wave equations

## Mathematical and Numerical Modelling of piezoelectric sensor

Justification of an approximate 3D model for piezoelectric sensors Piezoelectric sensors are widely used for ultrasonic non destructive testing as they can convert an elastodynamic wave into a difference of potential and vice versa, they are used both as emitter and receiver. The behavior of such devices is governed by Continue ReadingMathematical and Numerical Modelling of piezoelectric sensor

## Perfectly matched layers for wave equations

Perfectly matched layers for the water wave equation The water wave equations model gravity wave generation and propagation in water, in its complete form, it read as solving a homogeneous Laplacian problem in water coupled with a non linear boundary condition on the surface, depending on time. A simpler Continue ReadingPerfectly matched layers for wave equations