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Wave propagation in randomly layered media : properties and applications, R&D conférences

Presentation

Waves

1)    Main models of wave propagation: acoustic waves, wave equation, Schrödinger equations.

2)    Boundary conditions: physical boundaries, artificial boundary (transparent, absorbing boundary conditions, perfectly matched layers).

3)    Wave propagation in layered media: right and left going waves, reflection and transmission coefficients.

4)    Effective properties of randomly layered media: periodic and stochastic homogeneization.

5)    Introduction and numerical modeling of time reversal.

 

Organisation:

 

 

Waves

Before the lectures, students read a serie of documents available on the platform MOODLE and prepare answers to a serie of questions together with some numerical simulations. Synthesis during the lecture followed by additionnal labwork.

 

R&D

 

Conferences, mini-courses

 

Main difficulties for students:

 

Waves

 

Numerical implementation of boundary conditions.

Objectives

At the end of this module, the student will have understood and be able to explain (main concepts):

Waves

 

1)    The principle of transparent and absorbing boundary conditions for wave propagation.

2)    Periodic and stochastic homogeneisation

3)    Time Reversal.

 

R&D

The exposed R&D problem, the goals, the scientific and industrial approaches.

 

The student will be able to:

 

Waves

 

1)   Design theoretically and numerically transparent and absorbing boundary conditions.

2)   Model numerically wave propagation in layered media.

 

R&D

 

Fully understand the scientific and industrial approach, which are based on numerical modeling.

Needed prerequisite

Undergraduate level in mathematics and numerical analysis. Basic theory of partial differential equations.

Recommended prerequisite

Waves

Basics of PDE: methods of characteristics, finite difference methods for PDEs.

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...