Cours Master2/Cours Master2 2013

= Advanced Boundary Element Methods for Wave Propagation =

== Lecture 1: introduction ==
=== Lecture overview ===
* Useful references
*#Jean-Claude Nédélec, « [http://books.google.fr/books?id=NABGVMOHBqEC&printsec=frontcover&dq=Acoustic+and+Electromagnetic+Equations,+Integral+Representations+for+Harmonic+Problems&source=bl&ots=rhePtnlHUl&sig=rXUBozN7kFiqliSana81RkMhzPI&hl=fr&ei=k1w5TYWVEIat8QO-u9WuCA&sa=X&oi=book_result&ct=result&resnum=2&ved=0CCUQ6AEwAQ#v=onepage&q&f=false Acoustic and Electromagnetic Equations, Integral Representations for Harmonic Problems] », Applied Mathematical Sciences 144, Springer.
*# Isabelle Terrasse & Toufic Abboud, « [http://catalogue.polytechnique.fr/site.php?id=123 Modélisation des phénomènes de propagation d’ondes] », cours de l’école polytechnique.  
* Presentation of the course
** Introduction to the mathematical analysis of the diffraction problem
** Integral representation theorem
** Integral equations in the frequency domain
** Boundary Element Method in the Frequency Domain (FD BEM)
** Fast Multipole Method
** Integral equations in the time domain - Time domain BEM
** Current research and future trends
* Modeling
** acoustics
** electromagnetics
** elastodynamics
* Important issues
* Academic Examples
* Examples of applications in automotive and aeronautic industries
* Mathematical basis
** The single and double layer distributions
** The jump formula in 1D
** 1D Fourier transform: definition, main properties, causality
** Elementary solution: general concept, application to the Laplace operator in 3D, application to the Harmonic oscillator