Master 2 Course
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= Advanced Boundary Element Methods for Wave Propagation = | = Advanced Boundary Element Methods for Wave Propagation = | ||
| - | == Lecture 1: introduction | + | == Lecture 1: introduction == |
=== Lecture overview === | === Lecture overview === | ||
* Useful references | * Useful references | ||
| - | *#Jean-Claude Nédélec, « Acoustic and Electromagnetic Equations, Integral Representations for Harmonic Problems », Applied Mathematical Sciences 144, Springer. | + | *#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. | *# 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 | ||
| + | ** Fourier transform: definition, main properties, causality | ||
| + | ** Elementary solution: general concept, application to the Laplace operator in 3D, application to the Harmonic oscillator | ||
Version actuelle en date du 1 février 2013 à 00:11
Advanced Boundary Element Methods for Wave Propagation
Lecture 1: introduction
Lecture overview
- Useful references
- Jean-Claude Nédélec, « Acoustic and Electromagnetic Equations, Integral Representations for Harmonic Problems », Applied Mathematical Sciences 144, Springer.
- Isabelle Terrasse & Toufic Abboud, « 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
- Fourier transform: definition, main properties, causality
- Elementary solution: general concept, application to the Laplace operator in 3D, application to the Harmonic oscillator
