Advanced Boundary Element Methods for Wave Propagation

Lecture 1: introduction

Useful references
1. Jean-Claude Nédélec, « Acoustic and Electromagnetic Equations, Integral Representations for Harmonic Problems », Applied Mathematical Sciences 144, Springer.
2. 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 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